Study of Binimetinib With Encorafenib in Adults With Recurrent BRAF V600-Mutated HGG

Inclusion Criteria: 1. Patients receiving any other standard or investigational agents are ineligible. 2. Patients with history or current evidence of the following conditions are excluded: neuromuscular disorder with associated elevated CK (e.g. inflammatory myopathies, muscular dystrophy, amyotrophic lateral sclerosis, spinal muscular atrophy), pancreatitis, retinal vein occlusion, uncontrolled HIV, or Hepatitis B/C. An exception will be made for (HIV)-infected patients on effective anti-retroviral therapy with undetectable viral load within 6 months and for subjects with cleared HBV and HCV infections, who may enroll in the study. 3. Patients must have measurable (defined by at least 1 cm x 1 cm) contrast-enhancing disease by MRI imaging within 30 days of starting treatment. 4. The following intervals from previous treatments are required to be eligible: * 12 weeks from the completion of radiation. * 16 weeks from an anti-VEGF therapy * 4 weeks from a nitrosourea chemotherapy * 3 weeks from a non-nitrosourea chemotherapy * 2 weeks or 5 half-lives from any investigational (not FDA-approved) agents * 2 weeks from administration of a non-cytotoxic, FDA-approved agent (e.g., erlotinib, hydroxychloroquine, etc.) 5. Patients must be 18 years of age or older. 6. Patients must have a Karnofsky Performance (KPS) Status ≥ 60% 7. Patients must have adequate organ and marrow function within 30 days of starting treatment. 8. Patients must be able to provide written informed consent. 9. Women of childbearing potential must have a negative serum pregnancy test prior to study start. Women of childbearing potential must agree to use adequate contraception (intrauterine device, barrier, or other non-hormonal method of birth control; or abstinence) and not to donate ova from screening through 30 days after the last dose of study drug. Male participants must also agree to use adequate contraception and not to donate sperm from screening until 90 days after the last dose of study drug. 10. Patients must be maintained on a stable or decreasing dose of systemic corticosteroid regimen (no increase for 5 days) prior to baseline MRI. Topical and inhaled steroid treatment is allowed. 11. Patients must have no concurrent malignancy except curatively treated basal or squamous cell carcinoma of the skin or carcinoma in situ of the cervix, breast, or bladder. Patients with other malignancies must be disease-free for ≥ 2 years. 12. Patients must be able to swallow tablets and capsules. 13. Patients must have a tumor tissue form completed and signed by a pathologist (see Section 9.6.4). The tumor tissue form must indicate availability of archived tissue. The archived tissue should be from the most recent tumor resection, demonstrating active tumor when sufficient tissue is available. If sufficient tissue is not available from the most recent surgery, then tissue from an earlier surgery is acceptable, if available, including from the initial resection at diagnosis. Exclusion Criteria: 1. Patients receiving any other standard or investigational agents are ineligible. 2. Patients with history or current evidence of the following conditions are excluded: neuromuscular disorder with associated elevated CK (e.g. inflammatory myopathies, muscular dystrophy, amyotrophic lateral sclerosis, spinal muscular atrophy), pancreatitis, retinal vein occlusion, uncontrolled HIV, or Hepatitis B/C. An exception will be made for (HIV)-infected patients on effective anti-retroviral therapy with undetectable viral load within 6 months and for subjects with cleared HBV and HCV infections, who may enroll in the study. 3. Known hypersensitivity or contraindication to any component of binimetinib or encorafenib or their excipients 4. Current use of a prohibited medication (including herbal medications, supplements, or foods), or use of a prohibited medication ≤ 7 days prior to the start of study treatment. 5. Patient has not recovered to ≤ Grade 1 non-hematologic toxic effects of prior therapy before starting study treatment. Note: Stable chronic conditions (≤ Grade 2) that are not expected to resolve (such as neuropathy, myalgia, alopecia, prior therapy-related endocrinopathies) are exceptions and may enroll. 6. 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) ≤ 180 days prior to start date; * Congestive heart failure requiring treatment (New York Heart Association Grade ≥ 2); * Left ventricular ejection fraction (LVEF) \< 50% as determined by MUGA or ECHO; * Uncontrolled hypertension defined as persistent systolic blood pressure ≥ 150 mmHg or diastolic blood pressure ≥ 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 QTc interval ≥ 480 ms. 7. 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 (≤ 90 days) history of a partial or complete bowel obstruction, or other conditions that will interfere significantly with the absorption of oral drugs. 8. History of recent (≤ 90 days) thromboembolic or cerebrovascular event such as transient ischemic attack, cerebrovascular accident, or hemodynamically significant (massive or sub-massive) deep vein thrombosis or pulmonary emboli (DVT/PE). Note: Patients with DVT/PE that does not result in hemodynamic instability may enroll as long as they are anticoagulated for at least 4 weeks. Note: Patients with DVT/PE related to indwelling catheters or other procedures may enroll. 9. Patients with uncontrolled intercurrent illness including, but not limited to, ongoing or active infection or psychiatric illness/social situations that would limit compliance with study requirements, are ineligible. 10. Pregnant women are excluded from this study because the effects of encorafenib and/or binimetinib on a fetus are unknown. Because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with encorafenib or binimetinib, breastfeeding should be discontinued if the mother is treated with encorafenib and/or binimetinib. 11. Patients who previously received BRAF or MEK inhibitors are excluded (including but not limited to dabrafenib, vemurafenib, encorafenib, sorafenib, trametinib, binimetinib, cobimetinib, or selumetinib). 12. Patients will be excluded if their tumor harbors a known RAS activating mutation. This does not need to be specifically tested for eligibility. 3.4 Additional Inclusion Criteria for Surgical Arm Patients must meet the above inclusion / exclusion criteria for consideration with one exception. Patients with a BRAF-V600 E or K mutated low-grade glioma for whom there is a strong clinical suspicion of progression to high-grade would also be eligible for this arm. Additionally: 1. Patients must have a clinical indication for a tumor surgery. 2. No a priori contraindication to biospecimen collection (blood, tumor, CSF).