This phase 3 study is recruiting patients who have Essential Thrombocythemia (ET) who have an inadequate response to or are intolerant of hydroxyurea. This study will measure the safety and effectiveness of an inhibitor treatment called bomedemstat. Bomedemstat is an "investigational" (not yet FDA approved) treatment. The main purpose of the study is to how bomedemstat compares to BAT (best available therapy) as an effective treatment for ET. The study will enroll approximately 300 patients who will be randomly assigned 1:1 (like flipping a coin) to either bomedemstat or BAT. The study includes a screening phase, initial treatment phase, extended treatment phase, and posttreatment phase. The initial treatment portion of the study begins on study Day 1 and continues until the participant completes treatment at Week 52. The primary endpoint analysis will be performed on data from the first 52 weeks of treatment. Patients who have not discontinued study treatment at Week 52 will be eligible to continue receiving study treatment in the Extended Treatment Phase for up to Week 156. Patients in the BAT arm who have received a minimum of 52 weeks of treatment and discontinued study treatment due to intolerance/resistance/refractoriness/inadequate response (defined by the investigator as per the local product labels of BAT regimens) may be eligible to switch to the bomedemstat arm during the Extended Treatment Phase at the investigator's discretion (as per protocol defined eligibility to receive bomedemstat). Patients will continue treatment until disease progression, unacceptable toxicity, study closure, death, or withdrawal of consent. The main risk is that medical treatments often cause side effects. Patients may have none, some, or all of the side effects listed or not listed in the protocol, and they may be mild, moderate, or severe. There is no direct benefit for them in participating in this study.