Add the soy sauce, cornstarch, Chinese rice wine (Shaoxing Wine), and sesame oil to a medium mixing bowl. Whisk well to combine and add the chicken. Thoroughly coat the chicken with the soy sauce mixture. Cover and allow the chicken to marinate for at least 10 minutes, time permitting.
As the chicken marinates, prepare the sauce. In a medium bowl whisk together the Oyster sauce, soy sauce, chicken stock, brown sugar, Chinese rice wine (Shaoxing Wine), rice wine vinegar, cornstarch, and ground Szechuan peppercorns. Set aside.
Heat a large skillet or wok over high heat. Add 2 tablespoons of the cooking oil to the pan and allow it to get nice and hot. Add the chicken to the skillet, cooking for approximately 2-3 minutes before flipping and cooking on the other side (cooking time will vary depending on the size of your chicken pieces - avoid overcooking). Remove chicken to a clean plate and set aside.
Add the remaining 2 tablespoons of oil to the skillet set over medium-high heat. Add the garlic, ginger, white parts of the green onions, seeds from the dried chilies, and WHOLE dried chilies. Cook for approximately 30 seconds, stirring continuously.
Stir in the onion and bell peppers. Mix well to combine and cook for approximately 1-2 minutes, stirring often.
Return the chicken back to the pan, give the sauce a final stir and pour directly over the chicken and peppers. Stir continuously and bring the sauce to a low boil. You will notice that the sauce starts to thicken. Reduce heat and continue to cook, stirring continuously, until desired consistency is reached.
Remove from heat and add the green parts of the onions. Mix well to combine. Serve with your favorite rice or noodles.