Slice chicken into thin strips against the grain (it helps if it’s slightly frozen). Place in a large bowl.
In a separate bowl, whisk together chicken broth, soy sauce, cornstarch, and oil until smooth. Pour over the chicken and toss until evenly coated. Let marinate for 20 minutes.
Bring a large pot of water to a boil. Drain off the excess marinade, then add the chicken in batches. Cook just until the chicken turns white and is cooked through, about 2-3 minutes. Remove and set aside to drain.
In a small bowl, whisk together all sauce ingredients until smooth. Set aside.
Heat vegetable oil in a wok or large skillet over medium-high heat. Add dried Sichuan chiles and peppercorns (optional) and cook for about 1 minute until fragrant. Add garlic and ginger and cook another minute.
Add the velveted chicken, zucchini, green onions, and water chestnuts. Stir-fry for 3-4 minutes, until everything is heated through and the zucchini is crisp-tender.
Stir the sauce again, then pour it into the pan. Cook, stirring constantly, until the sauce thickens and coats everything.
Stir in the peanuts and serve hot over rice.