In a bowl, marinate the chicken with the light soy sauce, dark soy sauce, 1 1/2 teaspoons rice wine or dry sherry, pepper, and 3 teaspoons cornstarch, adding the cornstarch last. Let the chicken stand while preparing the other ingredients.
In a small bowl, combine the chicken broth or water, 1 1/2 teaspoons rice wine or dry sherry, sugar, and sesame oil. Whisk in 1 teaspoon cornstarch.
Heat a wok over medium-high heat and add 2 tablespoons oil. When the oil is hot, add half the ginger and garlic. Stir for about 10 seconds until aromatic, then add the chicken. Stir-fry the chicken for 2 to 3 minutes, until it turns white and is nearly cooked. Splash a bit of rice wine or dry sherry over the chicken while stir-frying if desired. Remove from the wok and drain in a colander or on paper towels. Clean out the wok.
Heat 1 tablespoon oil in the wok. Add the remainder of the ginger and garlic and stir for about 10 seconds until aromatic. Add the onion and green bell pepper. Stir-fry for a minute, then add the red bell pepper. Continue stir-frying for another minute, adding a bit of rice wine or dry sherry, chicken broth or water if the vegetables start to dry out.
Push the vegetables to the side and add the chicken. Stir briefly, then push to the sides. Re-stir the sauce and add it into the middle of the wok, stirring quickly to thicken. Stir to mix everything together. Stir in the green onion and serve hot over rice.
