In a bowl, combine the chicken pieces with salt, black pepper, soy sauce, oyster sauce, and cornstarch. Mix well and let marinate for at least 15 minutes.
Heat the vegetable oil in a large skillet or wok over medium-high heat. Add the marinated chicken 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 onion, bell pepper, garlic, and ginger. Stir-fry for about 3-4 minutes until the vegetables are tender.
Return the chicken to the skillet and pour in the chicken broth. Stir well to combine and cook for an additional 2-3 minutes until heated through.
Garnish with chopped green onions before serving.