Whisk all sauce ingredients in a small bowl until smooth. Set aside while you prep the rest of the ingredients. This ensures the sauce is ready to go when the chicken is cooked.
Add water to a nonstick skillet and bring to a boil. Add broccoli, cover, and simmer 2–3 minutes until crisp-tender. Drain and keep warm in a bowl tented with foil.
Heat oil in the same skillet, add chicken, season with salt and pepper, and cook until lightly browned. Stir occasionally to ensure even cooking and juicy bites.
Whisk the sauce again and pour over the chicken. Cook on medium-low heat, stirring occasionally until the sauce thickens and coats the chicken beautifully.
Spoon cooked rice into bowls, top with teriyaki chicken, broccoli, and avocado slices. Sprinkle with sesame seeds for a finishing touch.