For Chicken Coating, whisk together cornstarch, soy sauce, Shaoxing wine, and pepper in a large bowl. Mixture will be quite thick. Add chicken pieces to bowl; stir to coat chicken. Let stand at room temperature for 15 minutes.

Meanwhile, for Black Pepper Sauce, whisk together chicken broth, oyster sauce, Shaoxing wine, soy sauce, water, cornstarch, and pepper in a medium bowl.

Heat 2 tablespoons vegetable oil in a 12-inch skillet over medium-high heat. Add half the chicken. Cook and stir until lightly browned and no longer pink, about 5 minutes. Transfer chicken to a plate; set aside. Repeat with remaining chicken. Remove chicken from skillet.

Add remaining 1 tablespoon vegetable oil to skillet. Stir in bell pepper and onion. Cook and stir until crisp-tender, 2 to 3 minutes. Add garlic and ginger halfway through. Cook and stir until fragrant, about 30 seconds.

Pour in Black Pepper Sauce and cook until sauce has thickened, 2 to 3 minutes. Return cooked chicken to skillet. Cook and stir until all ingredients are coated with sauce. Serve immediately over cooked white rice.