Marinate the chicken: In a medium bowl, combine chicken pieces with 1 tablespoon white wine, 1 tablespoon soy sauce, 2 teaspoons cornstarch, and 1 teaspoon sesame oil. Mix well to coat all pieces and let marinate for at least 20 minutes (or up to 1 hour for more flavor).
Prepare the sauce: In a small bowl, whisk together 1 tablespoon white wine, 3 tablespoons soy sauce, black vinegar, brown sugar, 1 teaspoon cornstarch, water, and 1 teaspoon sesame oil until completely combined. Set aside.
Heat your wok: Place a wok or large skillet over high heat. Add 1 tablespoon of vegetable oil and heat until shimmering.
Cook the chicken: Add the marinated chicken to the hot wok in a single layer. Cook undisturbed for 1 minute, then stir-fry until golden brown and cooked through, about 3-4 minutes. Remove chicken to a clean plate.
Infuse the oil: Add remaining 2 tablespoons of oil to the wok. Add dried chili peppers and Sichuan peppercorns (if using). Stir-fry for 30 seconds until fragrant but not burned.
Add aromatics: Add minced garlic, ginger, and white parts of green onions. Stir-fry for 30 seconds until fragrant.
Cook the vegetables: Add diced bell pepper and zucchini (if using). Stir-fry for 1-2 minutes until vegetables begin to soften but still maintain some crispness.
Combine everything: Return cooked chicken to the wok. Add peanuts and green parts of green onions.
Add the sauce: Give your sauce mixture a quick stir, then pour into the wok. Stir-fry everything together for 1-2 minutes until the sauce thickens and coats all ingredients evenly.
Serve immediately: Transfer to a serving plate and enjoy hot with steamed rice.