* Participants must have histologically confirmed LGG World Health Organization (WHO) Grade I or II with BRAF V600 mutation confirmed by immunohistochemistry or sequencing
* Participants must have measurable tumor.
* For participants with measurable disease, this will be defined as lesions that can be accurately measured in two dimensions (longest diameter to be recorded) with a minimum size of no less than double the slice thickness. Previously irradiated lesions are considered non-measurable except in cases of documented progression of the lesion since the completion of radiation therapy. Participants without measurable disease may be considered for enrollment and followed for survival and progression purposes but will not be included as part of a measurable disease cohort.
* Cohort 1:
* Participants must have no prior therapy, except for surgical intervention (i.e. biopsy or resection)
* Participants may currently be taking dabrafenib and trametinib as frontline therapy, with a maximum duration of 21 months and participants must not yet have met criteria for confirmed best response as defined in this protocol. For participants entering the trial currently taking dabrafenib and trametinib, they must be taking a dose that is within 20% of the standard dosing for both drugs based on age and weight. Participants who are already on dabrafenib and trametinib when enrolling on trial and whose dosing deviates more than 20% from the protocol nomogram need to be discussed with the study chairs. Eligibility for these participants will be based on ability to wean within the parameters of the protocol
* Cohort 2:
* Participants must have a history of recurrent or progressive disease following prior therapy (e.g., carboplatin and vincristine, vinblastine, bevacizumab, mitogen-activated extracellular signal-regulated kinase (MEK) inhibitor, radiation therapy etc). Participants who previously completed a course of therapy with dabrafenib and trametinib, who did not progress on this therapy, and who are beyond 6 months from completion of therapy are eligible for retreatment.
** Participants may currently be taking dabrafenib and trametinib as therapy for disease recurrence, for a maximum duration of 21 months and participants must not yet have met criteria for confirmed best response as defined in this protocol. For participants entering the trial currently taking dabrafenib and trametinib, they must be taking dose that is within 20% of the standard dosing for both drugs based on age and weight. Participants who are already on dabrafenib and trametinib when enrolling on trial and whose dosing deviates more than 20% from the protocol nomogram need to be discussed with the study chairs. Eligibility for these participants will be based on ability to wean within the parameters of the protocol
* Participants must have received their last dose of chemotherapy 3 weeks prior to enrollment (6 weeks for nitrosoureas) and recovered from acute adverse events due to agents administered
* Participants must be at least 7 days since the completion of therapy with a biologic or small molecule agent except dabrafenib and trametinib. For any agent with known adverse events that can occur beyond 7 days after administration, the period prior to enrollment must be beyond the time during which adverse events are known to occur. Such participants must be discussed with study chairs
* Radiation:
* No prior radiation is allowed for participants in Cohort 1
* Participants in Cohort 2 must have:
* Had their last fraction of local irradiation to primary tumor ≥ 12 weeks prior to registration
* Had their last fraction of craniospinal irradiation ≥ 12 weeks prior to registration
* At least 14 days after local palliative radiation (small-port)
* Age: ≥ 12 months and < 25 years old
* Performance Score: Karnofsky ≥ 50 for participants > 16 years of age and Lansky ≥ 50 for participants ≤ 16 years of age. Participants who are unable to walk because of paralysis, but who are up in a wheelchair, will be considered ambulatory for the purpose of assessing the performance score
* Peripheral absolute neutrophil count (ANC) ≥ 1000/mm^3
* Platelet count ≥ 100,000/mm^3 (transfusion independent, defined as not receiving platelet transfusions for at least 7 days prior to enrollment)
* A serum creatinine ≤ 1.5 upper limit of normal (ULN) based on age and gender
* Total bilirubin ≤ 1.5 x ULN for age; in presence of Gilbert's syndrome, total bilirubin ≤ 3 x ULN or direct bilirubin ≤ 1.5 x ULN
* Alanine aminotransferase (ALT) ≤ 3 x ULN
* Aspartate aminotransferase (AST) ≤ 3 x ULN
* Participants with seizure disorder may be enrolled if well controlled
* Left ventricular ejection fraction (LVEF) greater than or equal to institutional lower limit of normal (LLN) by echocardiogram (ECHO) (while not receiving medications for cardiac function)
* Correct QT (QTc) interval < 480 msecs
* Patient must agree to adequate contraception. (The effects of dabrafenib and trametinib on the developing human fetus are unknown. For this reason and because agents as well as other therapeutic agents used on this trial are known to be teratogenic, women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method birth control, or abstinence) prior to study entry, for the duration of study participation, and 4 months after completion of the study medication administration. Should a women become pregnant or suspect she is pregnant while she or her partner is participating in this study, she should inform her treating physician immediately)
* A legal parent/guardian or patient must be able to understand, and willing to sign, a written informed consent and assent document, as appropriate
* Participants must enroll on Pediatric Neuro-Oncology Consortium (PNOC) comprehensive follow up protocol (PNOC COMP) if PNOC COMP is open to accrual at the enrolling institution
* Pathology reports, next generation sequencing reports, or both, confirming BRAF V600E mutation status must be submitted at the time of enrollment