In a large bowl, combine the chicken pieces with salt, black pepper, soy sauce, oyster 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 the chicken is browned and cooked through. Remove the chicken from the skillet and set aside.
In the same skillet, add the minced garlic and ginger. Sauté for about 30 seconds until fragrant.
Add the sliced bell peppers and onion to the skillet. Stir-fry for about 3-4 minutes until the vegetables are tender-crisp.
Return the cooked chicken to the skillet. Pour in the chicken broth and stir to combine. Cook for an additional 2-3 minutes, allowing the sauce to thicken slightly.
Garnish with sliced green onions before serving.