Vemurafenib and Cobimetinib in Treating Patients With BRAF V600E Mutation Positive Craniopharyngioma

* Pre-registration: Patients must have local diagnosis of papillary craniopharyngioma and have tissue slides available for submission to central pathology review; central pathology review will include immunohistochemistry (IHC) testing for BRAF V600E mutation (VE1 clone) and beta-catenin IHC (membranous, non-nuclear pattern) if needed to confirm diagnosis of papillary craniopharyngioma * Histologically proven papillary craniopharyngioma as documented by central pathology review with positive BRAF V600E mutation by IHC * Measurable disease and/or non-measurable disease * Measurable disease, defined as bidimensionally measurable lesions with clearly defined margins by magnetic resonance imaging (MRI) scans, with a minimum diameter of 10 mm in both dimensions * Progressive disease required in cohort B, defined as an increase in the bidirectional area by 25% within the past 13 months after surgery or radiation; progressive or recurrent disease is not required in cohort A, but is allowed provided it is a new diagnosis and patient has not received prior treatment. * Prior treatment * Cohort A: No prior therapy received other than surgery * Cohort B: Prior radiation therapy required (any type of prior radiation is allowed) * For patients treated with external beam radiation therapy, interstitial brachytherapy or radiosurgery, an interval of \>= 3 months must have elapsed from completion of radiation therapy to registration * Recovered to Common Terminology Criteri…