Virus-Based Gene Therapy (AdV-HSV1-TK and AdV-Flt3L) in Combination With Valacyclovir for the Treatment of Pediatric and Young Adult Patients With Resectable, Recurrent Primary Malignant Brain Tumors

Inclusion Criteria: * Age 3 to 25 years with: * Diagnosis of malignant primary brain tumor after tumor recurrence, relapse, or progression who have completed up-front, standard-of-care therapy * Age 26 to 39 years with: * Diagnosis of diffuse hemispheric glioma, H3 G34-mutant, per 2021 World Health Organization (WHO) classification, after tumor recurrence, relapse, or progression who have completed up-front, standard-of-care therapy * At least 10 kg (and body surface area \[BSA\] \> 0.5 m\^2) * Participants who are receiving corticosteroids must be on a stable or decreasing dose for at least 3 days prior to baseline MRI * Surgical resection of the tumor recurrence/relapse/progression is clinically indicated at the time of enrollment * A legal parent/guardian or patient must be able to understand, and willing to sign, a written informed consent and assent document, as appropriate * Participant must be willing to provide archival formalin-fixed embedded (FFPE) and/or frozen tissue specimens, if available * Participant must have recovered from all acute side effects of prior therapy. * From the projected start of scheduled study treatment, the following time periods must have elapsed: At least 7 days after last dose of a biologic agent or beyond time during which adverse events are known to occur for a biologic agent, 5 half-lives from any investigational agent, 4 weeks from cytotoxic therapy (except 23 days for temozolomide and 6 weeks from nitrosoureas), 6 weeks from antibody therapy (21 days for bevacizumab,.6 weeks from cellular therapy (i.e. modified T cells, natural killer \[NK\] cells, dendritic cells, etc.), or 4 weeks (or 5 half-lives, whichever is shorter) from other antitumor therapies * For participants who have received radiotherapy previously, participants must be at least 28 days from focal radiation therapy, at least 150 days from craniospinal irradiation therapy. * The use of bevacizumab to control radiation therapy-induced edema is allowed prior to or during study therapy (if used for tumor-directed therapy, please see required washout period above). * Dosing limitations are as follows: * Bevacizumab (or bioequivalent) for up to a maximum of 5 doses, dosing per institutional standard. There is no required washout period * Prior use of temozolomide during radiation at maximum of the standard pediatric dosing (defined as 90 mg/m\^2/dose continuously during radiation therapy) or dexamethasone is allowed * Peripheral absolute neutrophil count (ANC) ≥ 1000/mm\^3 (1.0g/l) * Platelet count ≥ 100,000/mm\^3 (100x10\^9/l) (transfusion independent, defined as not receiving platelet transfusions for at least 7 days prior to enrollment) * Creatinine clearance or radioisotope glomerular filtration rate (GFR) ≥ 70mL/min/1.73 m\^2 or a serum creatinine within the normal limits for age * Bilirubin (sum of conjugated + unconjugated) ≤ 2 x upper limit of normal (ULN) for age * Alanine aminotransferase (ALT) (serum glutamic pyruvic transaminase \[SGPT\]) ≤ 3 x ULN * Serum albumin ≤ 2 g/dL * Performance score ≥ 60 (Karnofsky for participants \> 16 years of age, Lansky 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 * The effects of the study drugs on the developing human fetus are unknown. For this reason, females of child-bearing potential (FOCBP) and males must agree to use adequate contraception for the duration of study participation and 30 days after last dose of AdV-HSV1-TK/AdV-Flt3L or valacyclovir, whichever is later. * Adequate methods include hormonal or barrier method of birth control, or abstinence at the time of study entry and for the duration of study participation. * Should a participant become pregnant or suspects she is pregnant while participating in this study, she should inform her treating physician immediately. * Males treated on this study must also agree to use adequate contraception as of the time of enrollment onto the study and for the duration of study participation. Male participants must notify the treating physician immediately if his partner becomes pregnant while he is receiving study therapy Exclusion Criteria: * Patient deemed not clinically appropriate to undergo tumor tissue resection by a neurosurgeon * Evidence of disseminated disease, including diffuse leptomeningeal disease or evidence of cerebrospinal fluid (CSF) dissemination * Patient with primary brainstem or primary spinal tumors * History of prior gene therapy * Ongoing therapy with valacyclovir that is unable to be stopped due to a medical condition * Known allergy to valacyclovir * Concurrent use of other investigational agents. * Participants who are currently receiving another investigational drug. Investigational imaging agents or agents used to enhance tumor visibility on imaging or during tumor biopsy/resection should be discussed with the study chairs * Participants who are currently receiving anti-cancer agents * Participants with a known disorder that affects their immune system, such as HIV or hepatitis B or C, or an auto-immune disorder requiring systemic cytotoxic or immunosuppressive therapy * Presence of uncontrolled infection or other uncontrolled systemic illness * Current diagnosis of bipolar disorder or major depressive disorder * Presence of a congenital immune deficiency syndrome or acquired autoimmune disease * Female participants of childbearing potential must not be pregnant or breast-feeding. Female participants of childbearing potential must have a negative serum or urine or serum pregnancy test prior to the start of therapy (as clinically indicated) * Active illicit drug use or diagnosis of alcoholism * History of kidney transplant * History of allogeneic stem cell transplantation * Known additional malignancy that is progressing or requires active treatment within 3 years of start of study drug