This clinical trial evaluates how well two surgical procedures (bilateral salpingectomy and bilateral salpingo-oophorectomy) work in reducing the risk of ovarian cancer for individuals with BRCA1 mutations. Bilateral salpingectomy involves the surgical removal of fallopian tubes, and bilateral salpingo-oophorectomy involves the surgical removal of both the fallopian tubes and ovaries. This study may help doctors determine if the two surgical procedures are nearly the same for ovarian cancer risk reduction for women with BRCA1 mutations.

PRIMARY OBJECTIVE: I. To compare the non-inferiority of bilateral salpingectomy (BLS) with delayed oophorectomy to bilateral salpingo-oophorectomy (BSO) to reduce the risk of ovarian cancer among individuals with deleterious BRCA1 germline mutations. SECONDARY OBJECTIVES: I. To prospectively assess estrogen deprivation symptoms in pre-menopausal BLS patients as measured by the Functional Assessment of Cancer Therapy - Endocrine Symptom (FACT-ES) subscale compared to pre-menopausal patients in the BSO arm. II. To determine if health-related quality of life (QOL) (FACT) is negatively impacted by menopausal symptoms (menopausal symptom checklist-Menopausal Symptom Checklist \[MSCL\]) and sexual dysfunction (Female Sexual Function Index \[FSFI\]) in pre-menopausal patients who have undergone BLS, in comparison to normative data (MSCL/FACT-ES) and data from pre-menopausal BSO patients. III. To determine if health-related QOL (FACT) is negatively impacted by cancer distress (Impact of Event Scale \[IES\]) in individuals who have undergone BLS, in comparison to BSO patients. IV. To assess medical decision making, as measured by the Shared Decision Making Questionnaire (SDM-Q-9) and Decision Regret Scale (DRS), and determine factors associated with the risk of reducing surgical treatment choice. V. To assess adverse events, graded using Common Terminology Criteria for Adverse Events (CTCAE) version (v)5.0. EXPLORATORY OBJECTIVES: I. Sexual dysfunction, as measured by selected Patient-Reported Outcomes Measurement Information System (PROMIS) screener and external sexual function items (pre-menopausal patients). II. To estimate the cost-effectiveness of BLS compared to BSO for ovarian cancer risk reduction. III. To assess medical decision making, as measured by the Risk-Reducing Medical Decision Making (RR-MDM) survey, a targeted set of questions on risk reducing surgical treatment choice. TRANSLATIONAL RESEARCH OBJECTIVE: I. To bank tissue and blood biospecimens for future research. OUTLINE: Patients choose between 1 of 2 groups. GROUP I: Patients undergo bilateral salpingectomy. Patients may then undergo oophorectomy after initial surgery. GROUP II: Patients undergo bilateral salpingo-oophorectomy. Patients in both groups also undergo a pelvic or transvaginal ultrasound or pelvic magnetic resonance imaging (MRI) during screening and blood sample collection throughout the trial. After completion of study, patients are followed up at 10-60 days, 6, 12, and 24 months, and then annually for up to 20 years.