Heat the vegetable oil in a large skillet or wok over medium-high heat.
Add the sliced chicken to the skillet and cook for about 5-7 minutes, or until the chicken is browned and cooked through. Remove the chicken from the skillet and set aside.
In the same skillet, add the bell pepper, onion, and broccoli. Stir-fry for about 3-4 minutes until the vegetables are tender-crisp.
Add the minced garlic and ginger to the skillet and stir-fry for an additional 1-2 minutes until fragrant.
Return the cooked chicken to the skillet. Add the soy sauce, oyster sauce, and black pepper. Stir well to combine all ingredients.
If you prefer a thicker sauce, add the cornstarch mixture and stir until the sauce thickens, about 1 minute.
Serve hot over cooked white rice or noodles.