In a bowl, toss the chicken pieces with 1 tablespoon cornstarch until evenly coated.
Heat 2 tablespoons vegetable oil in a large skillet over medium-high heat. Add the coated chicken and cook until browned on all sides, about 4–5 minutes.
Add the red and green bell peppers and chopped onion to the skillet and stir-fry for 2–3 minutes until they begin to soften.
Stir in the minced garlic, minced ginger, dried red chilies, and crushed Szechuan peppercorns and cook for 1–2 minutes until fragrant.
Whisk together 3 tablespoons soy sauce, 1 tablespoon hoisin sauce, 1 teaspoon sesame oil, and 1 tablespoon brown sugar in a small bowl. Pour the sauce over the chicken and vegetables and stir to combine.
Continue cooking for about 4–5 minutes, stirring occasionally, until the sauce thickens slightly and the chicken is cooked through.
Remove from heat, garnish with chopped scallions, and serve hot.
