Prepare the Sauce: In a small bowl, mix soy sauce, oyster sauce, hoisin sauce, honey, cornstarch, and water. Set aside.
Cook the Chicken: Heat 1 tablespoon of oil in a large skillet or wok over medium-high heat. Add sliced chicken, season with black pepper, and cook until browned. Remove from the pan and set aside.
Stir-Fry the Broccoli: In the same pan, add the remaining oil and cook the broccoli for 2-3 minutes until it turns bright green and slightly tender.
Combine Everything: Add garlic and ginger to the pan, stirring for about 30 seconds until fragrant. Return the chicken to the pan.
Add the Sauce: Pour the prepared sauce over the chicken and broccoli. Stir well to coat everything evenly. Let it simmer for 2-3 minutes until the sauce thickens.
Final Touches: Drizzle with sesame oil and sprinkle with sesame seeds and sliced green onions. Serve hot over rice or noodles.