The Effects of Vemurafenib + Cobimetinib on Immunity in Patients With Melanoma

* Patients must have histological or cytological confirmed melanoma that is metastatic or that is unresectable stage III and clearly progressive. * Melanoma must be documented to contain a BRAFV600 mutation by a FDA approved assay * Age \> 18 years * ECOG PS 0,1, or 2 * Participants must have measurable melanoma. Measurable disease is defined as at least one lesion that can be measured accurately in at least one dimension (longest diameter to be recorded) as ≥ 20 mm with conventional techniques or as ≥ 10 mm with spiral CT scan. Cutaneous or subcutaneous lesions may be considered measurable if they can be measured reliably as ≥ 10 mm by direct physical exam measurement. In addition, participants must also have separate disease, which may or may not be measurable as defined by RECIST, but must be readily accessible for core needle biopsy, excisional biopsy, and/or surgical resection. This disease may include one large tumor tissue deposit from which biopsies can be harvested multiple times or may include multiple deposits which can be biopsied, or excised individually, on different dates. Please see below for suggested minimum size requirements of tumor tissue to be used for biopsy for research: * 1 lesion ≥ 5 cm3 or * 2 lesions ≥ 3 cm3 each * 3 lesions ≥ 2 cm3each OR * ≥ 3 skin lesions, such that the surface area is approximately 1 cm\^2 each (or in aggregate for several lesions) and the total volume of tumor I s approximately 260-325 mm\^3 or greater for each biopsy time point. These subjects will need ≥ 3 such epidermal/dermal tumor lesions; excisional tumor tissue biopsies will be performed on one or more lesions at each time point. It is acceptable to biopsy more than one lesion, that may be less than 1 cm\^2 in surface area, as long as the total tissue removed has a surface area of approximately 1 cm\^2 or greater. * A combination of these may be acceptable, as long as there appears to be enough tumor tissue to remove approximately 325 mm\^3 or more of tissue at each time point. Lesion volume can be calculated based on the formula for volume of a sphere (4/3 r3). An acceptable approximation for lesions approaching spherical shape is to multiply the diameters in three perpendicular directions and divide by 2. \[Volume \~ ½(D1xD2xD3); e.g.: volume of a 2 x 2 x 3 cm lesion is approximately 6 cm3. Lesion measurements are based on length X width X depth (height) of sample.\] * Women must not be pregnant due to the fact that the effects of vemurafenib and/or cobimetinib on the developing human fetus are unknown. For this reason, women of childbearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry, for the duration of study participation and for 6 months after completion of study treatment. See Appendix H for acceptable and unacceptable forms of contraception. Should a woman become pregnant while participating in this study, she should inform her treating physician immediately. * All females of childbearing potential must have a blood test or urine study within 2 weeks prior to registration to rule out pregnancy. A female of childbearing potential is any woman, regardless of sexual orientation or whether they have undergone tubal ligation, who meets the following criteria: 1) has not undergone a hysterectomy or bilateral oophorectomy; or 2) has not been naturally postmenopausal for at least 24 consecutive months (i.e., has had menses at any time in the preceding 24 consecutive months). * Because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with vemurafenib and/or cobimetinib, breastfeeding must be discontinued prior to treatment Day 1 of the study. * Patients must have measurable disease as defined in Section 9.1. Cutaneous lesions or lymph nodes measuring at least 1 cm will be considered measurable. Baseline CT or MRI scans of measurable disease sites must be performed within 4 weeks of study entry. * Patients may have received any number of prior systemic treatment regimens for distant metastatic disease or advanced regional disease. The following prior therapy is permitted in either the adjuvant or metastatic disease setting: 1. No prior therapy 2. Immunotherapy consisting of interferon-alpha, interleukin-2, GM-CSF, ipilimumab, anti-PD1, cancer vaccines, or other experimental agent. 3. Cytotoxic chemotherapy consisting of dacarbazine, temozolomide, carboplatin, or paclitaxel alone or in combination. 4. Targeted therapy with temsirolimus, bevacizumab, or sorafenib. * Patients who have had prior therapy with a MEK inhibitor or an inhibitor of mutant BRAF are ineligible. Because sorafenib has low efficacy as a BRAF inhibitor, prior therapy with it is allowed. * Patients must have discontinued cytotoxic therapy agents at least 4 weeks and cytokine and immunoregulatory antibody based immunotherapy at least 6 weeks prior to entering the study and have recovered from adverse events due to those agents. * Patients must be completed radiation therapy at least 4 week previously * Patients must have an ECOG performance status of 0, 1 or 2. * Patients must have the following baseline laboratory values: 1. White Blood Count \> 3,000/mm3 2. Absolute Granulocyte Count \> 1,500/mm3 3. Platelet Count \> 100,000/mm3 4. Hemoglobin \> 9 g/dL 5. Serum creatinine \< 1.5 x upper limit of normal (ULN) or serum creatinine clearance (CrCl) \> 40ml/min (CrCl= Wt (kg) x (140-age)\*/72 x Cr. level, \*female x 0.85) 6. AST and ALT \< 3 x ULN (\< 5 x ULN for patients with documented liver metastases) 7. Alkaline Phosphatase ≤ 2 x ULN (≤ 5x ULN for patients with known liver involvement and ≤ 7x ULN for patients with known bone involvement) 8. INR \< 1.5 and aPTT within 1.1 x ULN. Patients on warfarin therapy are not eligible due to the requirement for multiple biopsies. 9. Total Bilirubin \< 1.5 x ULN * Patients must not receive any other investigational agents during the period on study or the four weeks prior to entry. * Patients will be evaluated with a head CT or MRI within 4 weeks of enrollment. Patients must have no clinical evidence of active brain metastasis. Patients with a history of brain metastases must have had them treated greater than 4 weeks previously with the CNS lesions confirmed to be stable or regressing on imaging since the time of the last CNS treatment. Patients must have no residual neurologic symptoms while taking either no steroids or a stable dose of steroids for the 2 weeks prior to enrollment. Patients are allowed to be on a stable dose of anti-seizure meds. * Patients who have had brain metastases will be eligible only if all of the following are true: * the total number of brain metastases ever is ≤ 3 * all are less than or equal to 2 cm * they have been resected surgically or have been treated with gamma-knife or stereotactic radiosurgery * the patient has not taken any steroids or has not increased the dose of steroids ≤ 14 days prior to registration. * Patients must not have another cancer diagnosis with a few exceptions- the following diagnoses will be allowed: 1. squamous cell cancer of the skin without known metastasis. Note, patients with suspected cuSCCs should have them excised prior to study registration. 2. basal cell cancer of the skin without known metastasis 3. carcinoma in situ of the breast (DCIS or LCIS) 4. carcinoma in situ of the cervix 5. any cancer without distant metastasis that has been treated successfully, without evidence of recurrence or metastasis for over 3 years * Patients must not have a serious intercurrent illness including, but not limited to: * Ongoing or active infection requiring parental antibiotics on Day 1 * History of congenital long QT syndrome or mean corrected QTc interval \> 450 msec at baseline * Clinically significant cardiovascular disease: Myocardial infarction within 6 months Unstable angina New York Heart Association grade II or greater congestive heart failure (see Appendix E) Serious cardiac arrhythmia requiring medication Uncontrolled hypertension ≥ Grade 2 (patients with a history of hypertension controlled with anti-hypertensives to ≤ Grade 1 are eligible) Left ventricular ejection fraction (LVEF) below institutional lower limit of normal or below 50% * Serious, non-healing wound, active ulcer, or untreated bone fracture * Psychiatric illness/social situations that would limit compliance with study requirements. * Participants must not be known to be HIV positive (testing is not required) * Participants must be Hepatitis C negative \< 6 months prior to screening * Participants must not have a history of malabsorption or other condition that would interfere with absorption of vemurafenib or cobimetinib * Patients must be able to comply with study and follow-up procedures. * Patients must not have following foods/supplements at least 7 days prior to initiation of and during study treatment: St. John's wort or hyperforin (potent cytochrome P450 CYP34A enzyme inducer) or Grapefruit juice (potent cytochrome P450 CYP34A enzyme inhibitor). * Patients must not have significant ocular issues including history of or evidence of retinal pathology on ophthalmologic examination that is considered a risk factor for neurosensory retinal detachment, RVO, or neovascular macular degeneration. The risk factors for RVO are listed below. Patients should be excluded if they have the following conditions: 1. Uncontrolled glaucoma with intra-ocular pressures \> 21mmHg 2. Serum cholesterol ≥ Grade 2 3. Hypertriglyceridemia ≥ Grade 2 4. Hyperglycemia (fasting) ≥ Grade 2 * Patients must have the ability to understand and the willingness to sign a written informed consent document.