Inclusion Criteria:
* Arms A \& B: Recurrent high grade glioma (2021 WHO Grades 3 and 4), defined as participants who have progressed on or following standard therapy, which includes maximal surgical resection, temozolomide, and fractionated radiotherapy.
* Arm C, D, \& E: Newly diagnosed glioblastoma (2021 WHO Grade 4), who have not received any tumor directed intervention other than biopsy or resection.
* Candidate for clinical resection of rHGG (Arms A \& B) or nGBM (Arms C \& D).
* Adequate archival or biopsy tissue available for testing of EGFR alterations. The tissue must have evidence of EGFR alterations including variants, fusion, and mutations with or without amplifications. rHGG participants with EGFR fusion will be solely enrolled into Arm B.
* Participants must have measurable disease preoperatively, defined as at least 1 contrast-enhancing lesion, with 2 perpendicular measurements of at least 1 cm.
* Provision of signed and dated, written informed consent (personally or by the legally authorized representative, if applicable) prior to any study specific procedures, sampling and analyses.
* Age ≥ 18 at time of consent
* Have a performance status (PS) of ≤ 2 on the Eastern Cooperative Oncology Group (ECOG) scale.
* Ability to swallow oral medications.
* Participant has adequate bone marrow and organ function as defined by the following laboratory values (as assessed by the local laboratory for eligibility):
* Absolute neutrophil count ≥ 1,500/mcL
* Platelets ≥ 100,000/mcL (at time of surgery)
* Hemoglobin ≥ 8.5 g/dL (Participants may receive erythrocyte transfusions to achieve this hemoglobin level at the discretion of the investigator. Initial treatment must not begin earlier than the day after the erythrocyte transfusion.)
* Total bilirubin ≤ 1.5 X ULN (Participants with Gilbert's syndrome with a total bilirubin ≤ 3.0 times ULN and direct bilirubin within normal limits are permitted.)
* AST (SGOT) ≤ 3 X institutional ULN
* ALT (SGPT) ≤ 3 X institutional ULN
* Serum creatinine ≤ 1.5 X ULN or estimated creatinine clearance ≥ 60 mL/min (calculated using Institutional standard method)
* Participants on corticosteroids at baseline must be on stable or decreasing doses for at least 5 days prior to Day 1.
* Confirmed negative serum pregnancy test (β-hCG) before starting study treatment or participant who is no longer of childbearing potential due to surgical, chemical, or natural menopause.
* For females of reproductive potential: use of highly effective contraception and agreement to use such a method during study participation until the end of treatment administration and for 16 weeks after the last dose of study drug.
* For males of reproductive potential: use of condoms or other methods to ensure effective contraception with partner until the end of treatment administration and for 16 weeks after the last dose of study drug.
* Agreement to adhere to Lifestyle Considerations throughout study duration.
Exclusion Criteria:
* Pregnancy or breastfeeding.
* Known allergic reactions to components of the BDTX-1535.
* Known to have active (acute or chronic) or uncontrolled severe infection, liver disease such as cirrhosis, decompensated liver disease, and active and chronic hepatitis, as determined by the investigator.
* Known active systemic bacterial infection (requiring intravenous \[IV\] antibiotics or fever \>38.5°C at time of initiating study treatment), fungal infection, or detectable viral infection (such as known human immunodeficiency virus positivity or with known active hepatitis B or C \[for example, hepatitis B surface antigen positive\]. Screening of viral infection is not required for enrollment.
* Significant cardiovascular disease, including NYHA Class III or IV congestive heart failure, myocardial infarction, unstable angina, poorly controlled cardiac arrhythmias, or stroke in the preceding 6 months prior to study Day 1.
* Symptomatic or radiographic leptomeningeal disease.
* Participant has serious and/or uncontrolled preexisting medical condition(s) that, in the judgment of the investigator, would preclude participation in this study (for example, interstitial lung disease, severe dyspnea at rest or requiring oxygen therapy, severe renal impairment \[e.g. estimated creatinine clearance \<30ml/min\], history of major surgical resection involving the stomach or small bowel, or preexisting Crohn's disease or ulcerative colitis or a preexisting chronic condition resulting in baseline Grade 2 or higher diarrhea).
* Concurrent use of prohibited medications: coadministration of strong CYP2C8 and CYP3A4 inhibitors and inducers with BDTX-1535. These should be discontinued 1 week or 5 half-lives (whichever is greater) prior to study Day 1. Strong inhibitors of P-gp (e.g., Amiodarone, carvedilol, dronedarone, propafenone, quinidine, ranolazine, and verapami) and BCRP (e.g., curcumin, cyclosporin A, and eltrombopag) should be used with caution. Sensitive substrates of P-gp, BCRP, and OATP should also be used with caution.
* Therapeutic intent treatment with another investigational drug or other intervention within 5 half-lives of the investigational product whichever is longer.
* With the exception of alopecia, any unresolved toxicities from prior therapy greater than National Cancer Institute Common Terminology Criteria for Adverse Events (NCI-CTCAE v5) Grade 1 at the time of starting study treatment and patients with chronic Grade 2 unresolved toxicities may be eligible following discussion with the Principal Investigator.
