In a bowl, toss the cubed chicken breast with 1 teaspoon of cornstarch and a pinch of salt.
In a wok or large skillet, heat 2 tablespoons of oil over medium-high heat until hot but not smoking.
Add the chicken to the hot oil and stir-fry for about 5-7 minutes, until golden brown and cooked through. Remove and set aside.
In the same pan, add the sliced ginger and stir-fry for about 30 seconds until fragrant.
Add the halved mushrooms and zucchini to the pan. Stir-fry for about 4-5 minutes, until tender but still crisp.
Return the cooked chicken to the pan. Add soy sauce, oyster sauce, sugar, white pepper, and sesame oil. Stir well to coat everything.
In a small bowl, mix 2 tablespoons of water with 1 teaspoon of cornstarch until smooth. Pour into the pan and stir well. Cook for 1-2 minutes until sauce thickens slightly.
Taste and adjust seasoning with salt if necessary. Serve hot over steamed rice or alongside noodles.