Marinate the Chicken: In a medium bowl, combine the chicken pieces with 2 tablespoons of soy sauce and 1 tablespoon of cornstarch. Mix well to coat the chicken. Let it marinate for about 10-15 minutes.

Prepare the Sauce: In a small bowl, whisk together the oyster sauce, soy sauce, rice vinegar, sugar, and chicken broth or water. Set aside.

Cook the Chicken: Heat 1 tablespoon of vegetable oil in a large skillet or wok over medium-high heat. Add the marinated chicken and stir-fry for about 4-5 minutes, or until the chicken is browned and cooked through. Remove the chicken from the skillet and set it aside.

Sauté Vegetables: In the same skillet, add the remaining 1 tablespoon of vegetable oil. Add the sliced onion, green bell pepper, and red bell pepper. Stir-fry for about 3-4 minutes until the vegetables are tender-crisp. Add the minced garlic and freshly ground black pepper, and stir-fry for another minute.

Combine Chicken and Sauce: Return the cooked chicken to the skillet with the vegetables. Pour the sauce over the chicken and vegetables, stirring to coat everything evenly. Cook for another 2-3 minutes, or until the sauce thickens slightly and everything is heated through.

Serve: Garnish with chopped green onions if desired, and serve the black pepper chicken hot over cooked rice.