Inclusion Criteria:

          -  Pathologic findings supporting the clinical impression of anaplastic thyroid
             carcinoma. Diagnosis may include consistent with or suggestive of terminology
             associated with: anaplastic thyroid carcinoma, undifferentiated carcinoma, squamous
             carcinoma; carcinoma with spindled, giant cell, or epithelial features; poorly
             differentiated carcinoma with pleomorphism, extensive necrosis with tumor cells
             present

          -  Must have a BRAFV600E mutation-positive tumor, as determined by BRAF V600E
             immunohistochemistry on tumor tissue, genetic/molecular testing of tumor, or cell free
             (cf)NDA liquid biopsy

          -  Have measurable disease based on RECIST 1.1

          -  Total bilirubin =< 1.5 x upper limit of normal (ULN). Total bilirubin =< 3 x ULN for
             patients with Gilbert's syndrome

          -  Aspartate aminotransferase (AST) (serum glutamic-oxaloacetic transaminase
             [SGOT])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase [SGPT])
             =< 2.5 x ULN, (5 x ULN for patients with concurrent liver metastases)

          -  Serum creatinine =< within 1.5 x ULN

          -  Absolute neutrophil count (ANC) >= 1.0 x 10^9/L

          -  Platelets >= 100 x 10^9/L

          -  Hemoglobin >= 9.0 g/dL or 5.6 mmol/L

          -  International normalized ratio (INR) or prothrombin time (PT) =< 1.5 x ULN unless
             participant is receiving anticoagulant therapy as long as PT or activated partial
             thromboplastin time (aPTT) is within therapeutic range of intended use of
             anticoagulant

          -  Subjects must be willing to undergo tumor biopsy prior to and after the run-in with
             dabrafenib/trametinib (DT), unless in the opinion of the treating physician, a biopsy
             is not feasible or safe. Subjects must be willing to ultimately undergo surgery if
             their tumor becomes surgically resectable. Research subjects retain the right to
             refuse any research interventions

          -  Have an Eastern Cooperative Oncology Group (ECOG) performance status of 0 to 1.
             Evaluation of ECOG is to be performed within 7 days prior to the date of
             allocation/randomization

          -  The participant (or legally acceptable representative if applicable) provides written
             informed consent for the trial

          -  A male participant must agree to use a contraception of this protocol during the
             treatment period and for at least 8 months after the last dose of study treatment and
             refrain from donating sperm during this period

          -  A female participant is eligible to participate if she is not pregnant, not
             breastfeeding, and at least one of the following conditions applies:

               -  Not a woman of childbearing potential (WOCBP) OR

               -  A WOCBP who agrees to follow the contraceptive guidance during the treatment
                  period and for at least 6 months after the last dose of study treatment

        Exclusion Criteria:

          -  Significant cardiovascular impairment: history of congestive heart failure greater
             than New York Heart Association (NYHA) class II

          -  Untreated brain metastases

          -  Prior chemotherapy within < 1 week prior to study day 1 or patients who have not
             recovered (i.e., =< grade 2) from adverse events due to a previously administered
             agent, except for patients who have been on dabrafenib/trametinib (DT) according to
             the standard run-in outlined in the trial schema

          -  Has active autoimmune disease that has required systemic treatment in the past 2 years
             (i.e. with use of disease modifying agents, corticosteroids or immunosuppressive
             drugs). Replacement therapy (e.g., thyroxine, insulin, or physiologic corticosteroid
             replacement therapy for adrenal or pituitary insufficiency, etc.) is not considered a
             form of systemic treatment

          -  History of human immunodeficiency virus (HIV) or active hepatitis B (chronic or acute)
             or hepatitis C infection. Patients with past or resolved hepatitis B infection
             (defined as having a negative hepatitis B surface antigen [HBsAg] test and a positive
             anti-HBc [antibody to hepatitis B core antigen] antibody test) are eligible. However,
             patients with past or resolved hepatitis B virus (HBV) should be monitored for
             reactivation by a specialist. Patients positive for hepatitis C virus (HCV) antibody
             are eligible only if polymerase chain reaction (PCR) is negative for HCV ribonucleic
             acid (RNA). Note: no testing for HIV, hepatitis B and hepatitis C is required unless
             mandated by local heath authority

          -  Has a diagnosis of immunodeficiency or is receiving chronic systemic steroid therapy
             (in dosing exceeding 10 mg daily of prednisone equivalent) or any other form of
             immunosuppressive therapy within 7 days prior to the first dose of study drug

          -  Has received a live or live-attenuated vaccine within 30 days prior to the first dose
             of study drug. Administration of killed vaccines is allowed

          -  Has severe hypersensitivity (>= grade 3) to pembrolizumab and/or any of its excipients

          -  Has a history of (non-infectious) pneumonitis/interstitial lung disease that required
             steroids or has current pneumonitis/interstitial lung disease

          -  Has known psychiatric or substance abuse disorders that would interfere with
             cooperation with the requirements of the trial

          -  Females who are breastfeeding or pregnant at screening or baseline (as documented by a
             positive beta-human chorionic gonadotropin [beta-hCG] (or human chorionic gonadotropin
             [hCG]) test with a minimum sensitivity of 25 IU/L or equivalent units of beta-hCG [or
             hCG]). A women of childbirth potential (WOCBP) who has a positive urine pregnancy test
             within 72 hours prior to the first infusion will be excluded. If the urine test is
             positive or cannot be confirmed as negative, a serum pregnancy test will be required

          -  More than 30 days of DT therapy prior to enrollment

          -  A known history of retinal vein occlusion (RVO), central serous retinopathy (CSR),
             uncontrolled glaucoma or ocular hypertension