In a medium bowl, combine the chicken pieces, soy sauce, and cornstarch. Mix well and let marinate for 15 minutes.
Heat the vegetable oil in a large skillet or wok over medium-high heat. Add the marinated chicken and cook for about 5-7 minutes, or until browned and cooked through. Remove the chicken from the skillet and set aside.
In the same skillet, add the sliced mushrooms, bell pepper, onion, and garlic. Stir-fry for about 3-4 minutes, or until the vegetables are tender.
Return the cooked chicken to the skillet. Add the black pepper, salt, chicken broth, and oyster sauce (if using). Stir well to combine and cook for an additional 2-3 minutes, allowing the flavors to meld.
Serve hot, garnished with sliced green onions.