-  INCLUSION CRITERIA:

          -  Histologically confirmed diagnosis of HCL according to morphological and
             immunophenotypic criteria of WHO classification [WHO, 2008 revised 2016] of lymphoid
             neo

               -  Absolute neutrophil count (ANC) <1 x10(3)/mcL

               -  Hemoglobin <10g/dL

               -  Platelets<100 x10(3)/mcL

               -  Symptomatic splenomegaly

               -  Enlarging HCL mass > 2cm in short axis

               -  Leukemia cell count>5x10(3)/mcL

        Patients who have eligible blood counts within 4 weeks prior to initiation of study therapy
        will not be considered ineligible if subsequent blood counts prior to initiation of study
        therapy fluctuate and become ineligible up until the time of the initiation of study
        therapy.

          -  Patients must have BRAF V600 mutation as confirmed from fresh bone marrow aspirate,
             peripheral blood sample, or lymph node/mass by the Laboratory of Pathology, NCI. This
             may be done by PCR or sequence-based assays.

          -  Patients who are ineligible for, unable to obtain in a timely manner, cannot access,
             unwilling to undergo or have failed Moxetumomab Pasudotox trial at NCI

          -  Refractory or relapsed disease- defined as either:

               -  Refractory- no response or disease progression in <=1 year following first-line
                  treatment with a purine analog, or

               -  Relapsed- having relapsed following treatment with at least 1 prior purine-analog
                  treatment

          -  Age >=18 years

          -  ECOG performance status <=2 (Karnofsky >=60%)

          -  Patients must have adequate organ and marrow function as defined below:

               -  Total bilirubin <= 3x upper limit of normal (ULN), unless consistent with Gilbert
                  s (ratio between total and direct bilirubin > 5)

               -  AST and ALT <= 3x ULN

               -  Alkaline phosphatase < 2.5x ULN

               -  Serum creatinine <= 1.5 mg/dL or creatinine clearance >= 60 mL/min/1.73 m^2 for
                  patients with creatinine levels above institutional normal calculated using eGFR

               -  Serum albumin >= 2 g/dL

               -  Prothrombin time (PT)/International Normalized Ratio < 2.5x ULN (If on warfarin,
                  PT/INR < 3.5x ULN; If on any other anticoagulation, Prothrombin time (PT) < 2.5x
                  ULN

               -  Fibrinogen >= 0.5x lower limit of normal

          -  The effects of the study drugs on the developing human fetus are unknown therefore
             participants must use effective methods of contraception as directed below.

               -  Females of childbearing potential (FOCBP) who are sexually active with a
                  nonsterilized male partner must use a highly effective method of contraception
                  and not donate ova prior to study entry and or the duration of study treatment
                  and until 30 days after the last dose of study drug. Periodic abstinence, the
                  rhythm method, and the withdrawal method are not acceptable methods of
                  contraception. There is a potential for encorafenib to induce CYP3A4, which may
                  reduce the effectiveness of hormonal contraception methods. Therefore, the use of
                  at least 1 form of nonhormonal contraception is required for females of
                  childbearing potential during study

        treatment in this study. Females of childbearing potential are defined as those who are not
        surgically sterile (i.e., bilateral tubal ligation, bilateral oophorectomy, or complete
        hysterectomy) or those who are premenarchal or postmenopausal (defined as 12 months with no
        menses without an alternative medical cause). A highly effective method of contraception is
        defined as one that results in a low failure rate (i.e., less than 1% per year) when used
        consistently and correctly. Not all methods of contraception are highly effective. Should a
        woman become pregnant or suspect she is pregnant while she or her partner is participating
        in this study, she should inform her treating physician immediately.

        --Male participants must use a condom during treatment and through 90 days after the end of
        systemic exposure to study drug/treatment. If the male participant has a partner that is of
        child-bearing potential, the partner should also use contraception through

        90 days after the end of systemic exposure to study drug/treatment. In addition, male
        participants must refrain from donating sperm during the study treatment and through 90
        days after the end of systemic exposure to study drug/treatment. Males who have had a
        vasectomy qualify as having met the requirement for a highly effective birth control
        method.

          -  Ability of subject to understand and the willingness to sign a written informed
             consent document.

          -  Must co-enroll in study 10-C-0066: Collection of Human Samples to Study Hairy Cell and
             other Leukemias, and to Develop Recombinant Immunotoxins for Cancer Treatment

        EXCLUSION CRITERIA:

          -  Patients who have had chemotherapy, immunotherapy, investigational agent or
             radiotherapy within 4 weeks prior to the start of study treatment.

          -  Prior therapy with encorafenib and/or binimetinib

          -  Patients who are receiving any other investigational agents or have received an
             investigational agent within 14 days prior to the start of study treatment.

          -  Patients who have undergone major surgery less than or equal to 6 weeks prior to start
             of study treatment or who have not recovered from side effects of such procedure

          -  Known hypersensitivity or contraindication to any component of binimetinib or
             encorafenib or their excipients

          -  Inability to swallow and retain study drugs.

        Is pregnant or breastfeeding or expecting to conceive within the projected duration of the
        study treatment, starting with the screening visit. Pregnant women are excluded from this
        study because binimetinib and encorafenib have the potential for teratogenic

        or abortifacient effects. Because there is an unknown but potential risk for adverse events
        in nursing infants secondary to treatment of the mother with encorafenib and binimetinib,
        breastfeeding should be discontinued if the mother is treated.

          -  Uncontrolled intercurrent illness including, but not limited to, ongoing or active
             infection, cardiac dysfunction, uncontrolled pulmonary infection, pulmonary edema or
             psychiatric illness/social situations that would limit compliance with study
             requirements.

          -  Evidence of active Hepatitis B Virus (HBV) or Hepatitis C Virus (HCV) infection. Note:
             Patients with laboratory evidence of cleared HBV or HCV infection may be enrolled. If
             positive for Hepatitis B core antibody or surface antigen the patient must be on
             Tenofovir or Entecavir and Hepatitis B Viral deoxyribonucleic acid (DNA) load must be
             <2000 IU/mL

          -  Active second malignancy requiring treatment other than minor resection of indolent
             cancers like basal cell and squamous skin cancers.

          -  Human immunodeficiency virus (HIV)-positive patients unless taking appropriate
             anti-HIV medications with a CD4 count of > 200. Otherwise, there may be an increased
             risk of infections.

          -  History of an allogeneic bone marrow or stem cell transplant.

          -  Known history of acute or chronic pancreatitis.

          -  Impaired cardiovascular function or clinically significant cardiovascular disease
             including, but not limited to, any of the following:

               -  History of acute coronary syndromes (including myocardial infarction, unstable
                  angina, coronary artery bypass grafting, coronary angioplasty or stenting)
                  <3months prior to initiation of study therapy

               -  Congestive heart failure requiring treatment (New York Heart Association Grade
                  greater than or equal to 2);

               -  Left ventricular ejection fraction (LVEF) < 50% as determined by Multigated
                  Acquisition Scan (MUGA) or Transthoracic echocardiogram (TTE);

               -  Uncontrolled hypertension defined as persistent systolic blood pressure greater
                  than or equal to 160 mmHg or diastolic blood pressure greater than or equal to
                  100 mmHg despite current therapy;

               -  History or presence of clinically significant cardiac arrhythmias (including
                  resting bradycardia, uncontrolled atrial fibrillation or uncontrolled paroxysmal
                  supraventricular tachycardia);

               -  Triplicate average baseline QTcF interval greater than or equal to 480 ms.

          -  Impairment of gastrointestinal function or disease which may significantly alter the
             absorption of study drug (e.g., active ulcerative disease, uncontrolled vomiting or
             diarrhea, malabsorption syndrome, small bowel resection with decreased intestinal

        absorption), or recent (less than or equal to 3 months) history of a partial or complete
        bowel obstruction, or other conditions that will interfere significantly with the
        absorption of oral drugs.

          -  Concurrent neuromuscular disorder that is associated with elevated CK (e.g.,
             inflammatory myopathies, muscular dystrophy, amyotrophic lateral sclerosis, spinal
             muscular atrophy).

          -  History or current evidence of RVO or current risk factors for RVO (e.g., uncontrolled
             glaucoma or ocular hypertension, history of hyperviscosity or hypercoagulability
             syndromes); history of retinal degenerative disease.

          -  History of thromboembolic or cerebrovascular events less than or equal to 12 weeks
             prior to the first dose of study treatment. Examples include transient ischemic
             attacks, cerebrovascular accidents, hemodynamically significant (i.e. massive or
             sub-massive) deep vein thrombosis or pulmonary emboli. Note: Patients with either deep
             vein thrombosis or pulmonary emboli that does not result in hemodynamic instability
             are allowed to enroll as long as they are on a stable dose of anticoagulants for at
             least 4 weeks.

          -  Note: Patients with thromboembolic events related to indwelling catheters or other
             procedures may be enrolled

          -  Patients taking strong CYP3A4 inhibitors and strong/moderate CYP3A4 inducers