In a large skillet or wok, heat the vegetable oil over medium-high heat. Add the chicken pieces and cook until browned and cooked through, about 5-7 minutes. Remove the chicken from the skillet and set aside.
In the same skillet, add the sliced mushrooms, bell pepper, and onion. Stir-fry for about 3-4 minutes until the vegetables are tender.
Add the minced garlic and ginger to the skillet, cooking for an additional 1-2 minutes until fragrant.
Return the cooked chicken to the skillet. In a small bowl, mix the soy sauce, oyster sauce (if using), black pepper, cornstarch, and chicken broth. Pour this mixture over the chicken and vegetables.
Stir well to combine, cooking for another 2-3 minutes until the sauce thickens and everything is heated through.
Remove from heat and garnish with chopped green onions. Serve over cooked rice or noodles.