In a bowl, toss the cubed chicken with 1 teaspoon cornstarch and let it marinate for 10 minutes.
Whisk together soy sauce, oyster sauce, sugar, white pepper, sesame oil, 2 tablespoons water, and 1 teaspoon cornstarch to make the sauce; set aside.
Heat the wok or large skillet over medium-high heat and add the oil.
Add the peeled ginger slices and stir-fry briefly until aromatic, about 20–30 seconds.
Add the marinated chicken and stir-fry until the exterior turns white, about 2–3 minutes.
Add the halved mushrooms and zucchini pieces and continue stir-frying until the vegetables begin to soften, about 1–2 minutes.
Pour the prepared sauce into the wok and stir quickly until it thickens and evenly coats the chicken and vegetables, about 30–60 seconds.
Cook until the chicken is cooked through and the sauce is glossy, about 1 more minute; adjust salt to taste, then remove from heat and serve immediately.
