A Study of Panobinostat in Combination With Everolimus for Children and Young Adults With Gliomas

Inclusion Criteria: * All patients and/or a legal guardian must sign institutionally approved written informed consent and assent documents. * Patient must be greater than 2 years and less than 30 years * BSA (body surface area) greater than 0.3 m2 * Functional status: Karnofsky \> 50% for patients \> 16 years of age and Lansky \> 50% for patients \< 16 years of age (Karnofsky and Lansky is a scoring system used to quantify the general well being of cancer patients where 100% represents perfect health and 0% represents death). Neurologic deficits in patients with CNS tumors must have been relatively stable for a minimum of 7 days. Patients who are unable to walk because of paralysis, but who are able to sit in a wheelchair, will be considered ambulatory for the purpose of assessing the performance score. * Adequate bone marrow function * Adequate liver function * Adequate renal and metabolic function * Urine protein:creatinine (UPC) ratio of \< 1; or a urinalysis that is negative for protein; or 24-hour urine protein level \< 1000 mg/dL * Patients must have Magnesium \> 1.5 mg/dL and potassium \> 3.5 mmol/L * Patients with known seizure disorder must have seizures adequately controlled with non- enzyme inducing antiepileptic medications * No increase in steroid dose within the past 7 days. * STRATUM A: histological confirmation of a newly diagnosed high-grade glioma or DIPG or STRATUM B: histological confirmation of a recurrent or progressive grade II-IV glioma (including DIPG) \[histology can come from tissue at diagnosis or relapse\] * Primary brain or spine tumor are eligible, including tumors with metastases, multiple lesions * Patients must have fully recovered from the acute toxic effects of all prior chemotherapy, immunotherapy, or radiotherapy. * Myelosuppressive chemotherapy: Must not have received within 3 weeks (6 weeks if prior nitrosourea). * Hematopoietic growth factors: At least 7 days since the completion of therapy with a growth factor, 14 days for long-acting (e.g. PEG-filgrastim) * Biologic (anti-neoplastic agent): At least 7 days or 3 half-lives (whichever is longer) since the completion of therapy with a biologic agent. * Radiation therapy: Strata A: ≥ 2 weeks and ≤ to 12 weeks must have elapsed from radiation. Strata B: ≥ 2 weeks must have elapsed from focal radiation. * Surgery: \> 3 weeks from major surgery. If recent craniotomy, adequate wound healing must be determined by neurosurgical team. * Autologous Stem Cell Transplant or Rescue: No evidence of active graft vs. host disease and ≥ 4 weeks must have elapsed. * H3K27M mutation: Participants must have a mutation in H3.3 K27M or H3.1 K27M as identified by tumor (FFPE or fresh, diagnosis or relapse tissue, but relapse tissue preferred) sequencing, or by CLIA-certified immunohistochemistry staining positive for H3K27M, as defined by review by U of M neuro-pathology. Exclusion Criteria: * Patients who are breastfeeding, pregnant or refuse to use an effective form of birth control are excluded. Abstinence is considered an effective form of birth control. * Patients with uncontrolled infection are excluded. * Inability to swallow oral pill (panobinostat does not have liquid formulation). * Other medications: Patients receiving other anti-neoplastic agents are excluded; patients on enzyme-inducing anticonvulsive agents are excluded; patients requiring strong CYP3A4 or PGP inducers or inhibitors are excluded; patients on steroids for symptom management must be on a stable dose for 7 days prior to start of treatment. * Allogeneic stem cell transplant: Patients within 1 year of allogeneic stem cell transplant, patients with active GVHD or requiring immunosuppression are excluded. * Previous hypersensitivity to rapamycin or rapamycin derivatives. * Baseline QTc of \>450 msec on EKG OR electrolyte imbalance predisposing to QTc prolongation (baseline ≥ Grade 1 hypokalemia or hyperkalemia; and baseline ≥ Grade 2 Ca++, Mg++, phosphate abnormalities). Repletion/correction is allowed to achieve eligibility. Use of QTC prolonging medications will be monitored throughout the trial.