Combine the chicken pieces with the 1/4 cup corn starch, seasoning with salt and pepper as desired, ensuring the meat is well-coated. Warm the vegetable oil in a spacious skillet over high heat. Arrange the chicken in a single layer and sear for 3–4 minutes per side until each piece turns a rich golden hue; work in batches if necessary. Remove the cooked chicken and cover to maintain warmth. Introduce the onion, red bell pepper, and green bell pepper to the pan, then add the dried chilies and Sichuan peppercorns. Sauté for 3–4 minutes until the vegetables soften slightly. Stir in the minced garlic and ginger and cook for an additional 30 seconds until fragrant. Return the browned chicken to the skillet, mixing thoroughly with the vegetables. In a separate small bowl, whisk together the soy sauce, hoisin sauce, sesame oil, brown sugar, 1 tablespoon corn starch, and chicken broth until smooth. Pour this sauce over the chicken and vegetable medley. Bring the mixture to a vigorous boil and cook for 30 seconds to 1 minute until the sauce thickens to a glossy consistency. Serve immediately.