Coat the chicken pieces in corn starch, seasoning them lightly with salt and pepper. In a large, hot pan over high heat, pour in the vegetable oil and heat it thoroughly.
Carefully lay the chicken cubes in a single layer into the pan, allowing them to sear undisturbed for 3 to 4 minutes on each side, until crisp and golden. If needed, cook in batches to avoid overcrowding.
Once the chicken is browned, remove it from the pan and cover it to maintain warmth.
Toss the onion, red bell pepper, and green bell pepper into the same pan. Add the dried chilies and, if using, the sichuan peppercorns. Stir-fry for 3 to 4 minutes until the vegetables soften slightly.
Next, add the garlic and ginger to the pan, stirring for about 30 seconds until fragrant. Return the cooked chicken to the pan, combining it with the vegetables.
As the stir fry finishes cooking, prepare the sauce. In a small bowl, whisk together the soy sauce, hoisin sauce, sesame oil, brown sugar, chicken broth, and corn starch.
Pour the sauce over the chicken and vegetable mixture, bringing it to a simmer. Let it cook for 30 seconds to 1 minute, allowing the sauce to thicken slightly. Serve the dish immediately while hot.