A Study to Compare the Administration of Encorafenib + Binimetinib + Nivolumab Versus Ipilimumab + Nivolumab in BRAF-V600 Mutant Melanoma With Brain Metastases

Inclusion Criteria: * Participants must have histologically and pathologically confirmed melanoma that has metastasized to the brain * Any primary (cutaneous, acral/mucosal, etc) or unknown origin are permitted, except that participants with uveal primary are not eligible * Participants must have BRAF-V600 mutant melanoma documented by a Clinical Laboratory Improvement Act (CLIA)-certified laboratory * All participants must have an magnetic resonance imaging (MRI) of the brain within 28 days prior to registration and must have central nervous system metastases with at least one measurable brain metastasis \>= 0.5 cm in size (per modified RECIST 1.1) that has not been irradiated, or progressed (in the opinion of the treating physician) after prior radiation therapy. Participating sites MUST use MRI slice thickness of =\< 1.5 mm and are recommended to adhere to the 'minimum' Brain Tumor Imaging Protocol for Clinical Trials in Brain Metastases (BTIP-BM) compliant MRI acquisition protocol. Computed tomography (CT) of the head cannot substitute for brain MRI. (NOTE: All central nervous system \[CNS\] disease must be documented on BOTH the Brain Metastases Baseline Tumor Assessment Form, using modified RECIST, and the Baseline Tumor Assessment Form \[RECIST 1.1\] using RECIST 1.1.) * Participants may have measurable or non-measurable extracranial disease. All measurable disease must be assessed within 28 days prior to randomization; all non-measurable disease must be assessed with…