To marinate the chicken, in a bowl, combine the chicken with the salt and mix until absorbed. Add the soy sauce, dark soy sauce, and sugar. In a small bowl, combine the cornstarch and water to make a slurry, then add it to the chicken and mix well. Add the cooking oil and mix again. Let the chicken marinate while you prepare the remaining ingredients.
To prepare the vegetables, cube the onion, green bell pepper, and red bell pepper. Mince the garlic.
To make the black pepper sauce, in a small bowl, combine the cornstarch and water. Add the soy sauce, dark soy sauce, oyster sauce, black pepper, and chicken stock. Mix well until smooth.
To stir-fry the chicken, in a wok over high heat, add 1 tablespoon of cooking oil. Add the chicken and let it sear for about 20 seconds before stirring. Stir-fry for about 3 minutes until cooked through. Remove and set aside.
To stir-fry the vegetables, in the same wok over high heat, add the remaining tablespoon of cooking oil. Add the onion, green bell pepper, and red bell pepper. Stir-fry for about 30 seconds until slightly tender but still crisp. Add the garlic and stir-fry for about 10 seconds.
To finish the dish, return the chicken to the wok. Stir the sauce again, then pour it into the wok. Toss until the sauce thickens and evenly coats the chicken and vegetables. Serve immediately.