Toss the sliced chicken with soy sauce, cornstarch, sesame oil, and black pepper. Let it marinate for 10–15 minutes.
Whisk together the chicken broth, oyster sauce, soy sauce, brown sugar, cornstarch, and sesame oil. Set aside.
Heat the vegetable oil in a large skillet or wok over medium-high heat. Add the chicken and stir-fry for 4–5 minutes, until browned and cooked through. Remove and set aside.
Add the broccoli, mushrooms, and onion to the same pan. Stir-fry for 4–5 minutes, until the vegetables are crisp-tender.
Add the garlic and ginger and cook for 30 seconds.
Return the chicken to the pan and pour in the sauce. Toss well and cook for 2–3 minutes, until the sauce thickens and coats everything.
Serve hot over steamed rice or noodles.
Notes
For a spicier version, add red pepper flakes or sliced chili peppers.
Feel free to substitute other vegetables like bell peppers or snap peas.
This dish can be made ahead and reheated for a quick meal.