Toss the chicken with cornstarch, garlic powder, and ground ginger until evenly coated.
Heat 1 tablespoon of oil in a large wok over medium-high heat. Stir-fry the chicken for 6–8 minutes, until golden and cooked through. Add the soy sauce, toss to coat, then transfer the chicken to a plate.
Add the remaining oil to the wok. Stir-fry the carrot for 1–2 minutes, then add the zucchini and garlic. Cook for another 3–4 minutes, until the vegetables are crisp-tender.
Return the chicken to the wok and toss everything together. Stir in the peanuts and cook for another 1–2 minutes.
Garnish with green onions and serve immediately over rice or noodles.