Whisk together all sauce ingredients (except for water and corn starch) and set aside.
Drizzle a large skillet over medium heat with oil. Add chicken, season with Chinese five spice, and saute for 6-8 minutes until chicken is cooked through. Transfer to a plate and set aside.
Add broccoli florets to pan, saute 2-3 minutes until broccoli starts to become crisp on the edges. Add 1/3 cup water or chicken broth and cook for 4-6 minutes longer until broccoli is fork-tender.
Add chicken back to pan. Pour sauce into the pan and give it a good stir. Whisk together 1/2 cup cold water and corn starch until dissolved, then stir into the pan. Once sauce has thickened (about 1 minute) cook 2-3 minutes longer, then garnish with onions and sesame seeds and serve.
Spice it up: add 2-3 teaspoons of sriracha or 1/4-1/2 teaspoon of crushed red pepper flakes to give this recipe a spicy kick. Veg it up: add any favorite vegetable - like chopped bell peppers, onions, snow peas, or cauliflower.