Prepare sauce: In a small bowl, whisk together soy sauce, rice vinegar, hoisin sauce, chili garlic sauce, sugar, cornstarch, and water. Set aside.
Toast Szechuan peppercorns: Heat a large wok or skillet over medium heat. Add Szechuan peppercorns and dry toast for 30–60 seconds until fragrant. Remove and grind lightly if desired.
Cook chicken: Heat oil in the wok over high heat. Add chicken and stir-fry until lightly browned and almost cooked through. Remove chicken from wok and set aside.
Stir-fry vegetables: Add garlic, ginger, dried chilies, onion, and bell peppers to the wok. Stir-fry for 2–3 minutes until crisp-tender.
Combine: Return chicken to the wok. Pour in sauce and toss everything together. Cook for 2–3 minutes until sauce thickens and coats chicken and vegetables.
Add green onions and peppercorns: Toss in green onions and toasted Szechuan peppercorns, stir briefly, then remove from heat.
Serve immediately over steamed rice or noodles.