Pembrolizumab (MK-3475) and Bacillus Calmette-Guérin (BCG) as First-Line Treatment for High-Risk T1 Non-Muscle-Invasive Bladder Cancer (NMIBC) and High-Grade Non-Muscle-Invasive Upper Tract Urothelial Carcinoma (NMI-UTUC)]

Inclusion Criteria: * Be willing and able to provide written informed consent/assent for the trial. * Histologically confirmed urothelial cancer by TURBT performed at MSK for patients in the T1 bladder cancer cohort or by high-grade cytology/biopsy by ureteroscopy performed at MSK for patients in the NMI-UTUC cohort. * TURBT within 8 weeks of protocol entry with complete resection of all papillary lesions for patients in the T1 bladder cancer cohort and ureteroscopy within 8 weeks of protocol entry with complete ablation of all papillary lesions with ureteroscopy or through antegrade percutaneous access for patients in the NMI-UTUC cohort.. * Patients in the T1 bladder cancer cohort must have high risk, BCG-naïve non-muscle-invasive urothelial cancer defined as having one of the following disease states: * T1 on restaging biopsy, plus CIS * Multiple (≥ 1) T1 recurrences, plus CIS * Multifocal T1 plus CIS * T1b (extensive/deep invasion into lamina propria) plus CIS * Lymphovascular invasion plus CIS * T1 with variant histology: including micropapillary, nested variant, poorly differentiated, squamous, and glandular differentiation (the presence of variant histology will be based on MSKCC review), plus CIS. * T1 with urothelial carcinoma of prostatic urethra (Ta, Tis, or T1 within prostatic urethra), plus CIS * Large (≥3 cm) T1 tumor, plus CIS * Patients in the NMI-UTUC cohort must have high risk, BCG naïve NMI-UTUC, defined by having one of the following disease states: * Histologic confirmed ureteroscopic biopsy with clinical stage Tis (also known as CIS), Ta, or T1 disease in the renal pelvis. Concomitant ureteral disease will be allowed if completely treated endoscopically. * Clinical stage Tis confirmed by a positive high-grade selective cytology, coupled with ureteroscopic evaluation, confirming only flat eryethematous lesions and the absence of papillary tumors. * Must not have received prior treatment with percutaneous BCG to the involved renal unit, but prior intravesical BCG for bladder cancer is acceptable. * Patients must have cross sectional imaging (CT or MRI urogram) within 3 months of protocol entry demonstrating no evidence of metastasis or radiographic evidence of muscle invasive disease. * Patient refusal of cystectomy and bilateral pelvic lymphadenectomy for the T1 bladder cancer cohort, or refusal of radical nephroureterectomy for NMI-UTUC cohort. * No prior intravesical BCG therapy for patients in the T1 bladder cancer cohort. * No prior radiation therapy for bladder cancer for patients in the T1 bladder cancer cohort. Prior radiation therapy for prostate cancer is allowed. * ECOG performance status of 0 or 1. * Age ≥ 18 years. * Female subjects of childbearing potential must be willing to use 2 methods of birth control, be surgically sterile, or abstain from heterosexual activity for the course of the study through 120 days after the last dose of the study medication (reference section 9.5.2). Subjects of childbearing potential are those who have not been surgically sterilized or have not been free from menses for \>1 year. * Male subjects should agree to use an adequate method of contraception starting with the first dose of study therapy through 120 days after the last dose of study therapy. * Patients must not have other invasive malignancies within the past 5 years (with the exception of non-melanoma skin cancers, localized prostate cancer, and CIS of the cervix). * Required initial laboratory values: * Absolute neutrophil count ≥ 1.5 x 10\^9/L * Platelets ≥ 100 x 10\^9/L * Hemoglobin ≥ 9 g/dL * Bilirubin ≤ 1.5 times the upper limit of normal (x ULN) * Aspartate transaminase (AST) and alanine transaminase (ALT) ≤ 3.0 x ULN * Calculated creatinine clearance ≥ 30 using the CKD-Epi formula Exclusion Criteria: * Current or History of muscle invasive bladder cancer or prostatic stromal invasion. * Unstable angina * New York Heart Association (NYHA) Grade II or greater congestive heart failure * History of myocardial infarction within 6 months * History of stroke within 6 months * Evidence of bleeding diathesis or coagulopathy * Presence of any systemic metastases (i.e, nodal, visceral, or central nervous system) * Major surgical procedure (other than TURBT or ureteroscopy) within 28 days prior to the study * Pregnant (positive pregnancy test) or lactating * Serious, non-healing wound, ulcer, or bone fracture * Inability to comply with study and/or follow-up procedures * Prior therapy with an anti-PD-1 agent, anti-PD-L1 agent, or other inhibitory or stimulatory agent oriented towards a T-cell receptor * Active infection requiring systemic therapy * Known history of human immunodeficiency virus (HIV) * Known active Hepatitis B or Hepatitis C * Received live attenuated vaccines within 30 days prior to start of study treatment. Patients must also agree to avoid live attenuated vaccines during study treatment. * Has an active autoimmune disease requiring systemic treatment within the past 3 months or a documented history of clinically severe autoimmune disease, or a syndrome that requires systemic or immunosuppressive agents. Subjects with vitiligo, diabetes Type I, or resolved childhood asthma/atopy would be an exception to this rule. Subjects that require intermittent use of bronchodilators, inhaled steroids, or local steroid injections would not be excluded from the study. Subjects with hypothyroidism stable on hormone replacement or Sjøgren's syndrome will not be excluded from the study. * Known contraindications to BCG, defined as one of the following: * History of systemic hypersensitivity reaction or history of febrile systemic BCG reaction * Febrile illness or persistent gross hematuria * Active tuberculosis * Immunosuppression due to congenital or acquired immune deficiency, concurrent immune suppressive disease, systemic cancer therapy, or chronic immunosuppressive therapy other than topical or inhaled corticosteroids