Comparing two treatment combinations for 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 within 42 days prior to randomization. Please note, while any extracranial disease will also be assessed and followed, participants are NOT required to have extracranial disease for randomization. NOTE: All disease must be assessed and documented on the Baseline Tumor Assessment Form (RECIST 1.1). 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 leptomeningeal disease
* Participants may be receiving corticosteroids for brain metastases at a dose of up to 8 mg of dexamethasone per day. The dose must not have exceeded 8 mg per day for at least 7 days prior to randomization
* Participants must have Zubrod performance status =\< 2
* Participants must have complete history and physical examination within 28 days prior to randomization
* Participants must be able to swallow and retain pills
* Hemoglobin \>= 8.0 g/dL (within 28 days prior to randomization)
* Absolute neutrophil count \>= 1,500/mcL (within 28 days prior to randomization)
* Platelets \>= 75,000/mcL (within 28 days prior to randomization)
* Total bilirubin =\< 1.5 institutional upper limit of normal (ULN) (within 28 days prior to randomization)
* Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) =\< 2.5 x institutional ULN (in participants with liver metastases =\< 5 x ULN) (within 28 days prior to randomization)
* Creatinine =\< 2.0 institutional ULN (within 28 days prior to randomization)
* Participants with known history or current symptoms of cardiac disease, or history of treatment with cardiotoxic agents, must have a clinical risk assessment of cardiac function using the New York Heart Association Functional Classification. To be eligible for this trial, participants must be class 2B or better
* Participants with a prior or concurrent malignancy whose natural history or treatment (in the opinion of the treating physician) does not have the potential to interfere with the safety or efficacy assessment of the investigational regimen are eligible for this trial
* Participants with known human immunodeficiency virus (HIV)-infection are eligible providing they are on effective anti-retroviral therapy and have undetectable viral load at their most recent viral load test and within 90 days prior to randomization
* Participants with a known history of hepatitis C virus (HCV) infection must have been treated and cured. Participants with HCV infection who are currently on treatment must have an undetectable HCV viral load prior to randomization
* Participants must agree to participate in image banking. Images must be submitted via the Triad System
* Participants must be offered the opportunity to participate in specimen and blood collections
* Participants must be informed of the investigational nature of this study and must sign and give informed consent in accordance with institutional and federal guidelines
* As a part of the OPEN registration process the treating institution's identity is provided in order to ensure that the current (within 365 days) date of institutional review board approval for this study has been entered in the system

Exclusion Criteria:

* Participants must not have received prior systemic therapy for metastatic disease. Prior systemic therapy received only in the neoadjuvant and/or adjuvant setting (e.g., BRAF/MEK inhibitor therapy, anti-PD-1 therapy or anti-CTLA4 therapy, alfa-interferon, etc.) is permitted. If patients received prior neoadjuvant/adjuvant therapy, they must have had eventual disease relapse prior to randomization
* Participants must not have had prior radiation therapy within 7 days prior to randomization
* Participants must not be planning to require any additional form of systemic anti-tumor therapy for melanoma while on protocol treatment
* Participants must not be planning to use hormonal contraceptives
* Participants must not have a serious active infection requiring systemic therapy at time of randomization in the opinion of the treating physician
* Participants must not have active autoimmune disease that has required treatment in the past 6 months with use of biologic disease modifying agents (.e.g. infliximab, adalimumab). Patients on non-biologic disease modifying agents (e.g. methotrexate) or patients on corticosteroids =\< 10 mg prednisone daily or equivalent (to treat auto-immune disease), or on replacement therapy (e.g., thyroxine, insulin) are eligible if deemed in the best interest of the patient by treating physician
* Participants must not have had grade 3 or 4 immune-related adverse events on ipilimumab or nivolumab that required more than 12 weeks of immune suppression with corticosteroids
* Participants must not have had adverse events related to encorafenib and/or binimetinib specifically, that required discontinuation of one or both drugs. (Please note this does not apply to other BRAF/MEK inhibitor drugs.)
* Participants must not be pregnant or nursing. Women/men of reproductive potential must have agreed to use an effective method of contraception. (NOTE: Patients must agree to not use hormonal contraceptives, as encorafenib can result in decreased concentration and loss of efficacy.) A woman is considered to be of "reproductive potential" if she has had menses at any time in the preceding 12 consecutive months. In addition to routine contraceptive methods, "effective contraception" also includes heterosexual celibacy and surgery intended to prevent pregnancy (or with a side-effect of pregnancy prevention) defined as a hysterectomy, bilateral oophorectomy or bilateral tubal ligation. However, if at any point a previously celibate participant chooses to become heterosexually active during the time period for use of contraceptive measures outlined in the protocol, he/she is responsible for beginning contraceptive measures