In a medium bowl or large liquid measuring cup, stir together the sauce ingredients: 2/3 cup water, 1/3 cup reduced-sodium soy sauce, 3 tablespoons honey, 2 tablespoons rice vinegar, 2 tablespoons cornstarch, 3 cloves garlic (minced, about 1 tablespoon), 1 tablespoon minced fresh ginger, and 1/4 teaspoon red pepper flakes. Stir until the cornstarch is dissolved and the mixture is smooth.

Pour about one-third of the sauce into the bottom of a 6-quart or larger slow cooker. Reserve the remaining sauce.

Arrange 1 1/2 pounds boneless skinless chicken breasts on top of the thin layer of sauce. Pour the reserved sauce evenly over the chicken.

Cover the slow cooker and cook on LOW for 2 hours.

While the chicken cooks (or immediately after the 2-hour cook), combine 2 tablespoons cornstarch with 2 tablespoons water in a small bowl and stir to make a smooth slurry.

After 2 hours, uncover the slow cooker. Pour the cornstarch slurry into the liquid around the chicken. Add 2 heads broccoli, cut into florets, on top of the chicken and sauce.

Cover and change the slow cooker to HIGH. Cook until the broccoli is tender and the chicken registers 165°F with an instant-read thermometer, about 45 minutes to 1 hour more.

Remove the chicken from the slow cooker to a plate or cutting board. Let it cool briefly, then cut into bite-sized pieces.

Return the cut chicken to the slow cooker. Add 1 tablespoon toasted sesame oil and 1/2 cup chopped green onions. Stir gently to combine and smooth the sauce. Taste and add additional soy sauce or red pepper flakes to taste, if desired.

Serve the chicken and broccoli hot over cooked brown rice, quinoa, or cauliflower rice. Sprinkle with toasted sesame seeds before serving.