In a small bowl or large liquid measuring cup, stir together the sauce ingredients: water, soy sauce, honey, rice vinegar, cornstarch, garlic, ginger, and red pepper flakes. Pour a thin layer into the bottom of a 6-quart or larger slow cooker (about one-third of the sauce). Arrange the chicken breasts on top. Pour on the remaining sauce.
Cover the slow cooker and cook on LOW for 2 hours. In a small bowl, stir together the 2 tablespoons cornstarch with 2 tablespoons water to create a slurry, then add to the slow cooker, pouring into the liquid around the chicken. Add the broccoli florets on top. Cover and cook on HIGH, until the broccoli is tender and the chicken is fully cooked through and registers 165 degrees F on an instant read thermometer, about 45 minutes to 1 hour more.
Remove the chicken to a plate. Let cool, then cut into bite-sized pieces. Stir the broccoli around in the sauce to smooth the sauce out a bit. Return the chicken to the slow cooker and add the sesame oil and green onion. Stir to combine. Taste and adjust seasonings as desired. Serve hot over rice with a sprinkle of sesame seeds.
