In a bowl, marinate the chicken with soy sauce, cornstarch, and white pepper. Let sit for 20 minutes at room temperature.
While the chicken is marinating, prep the vegetables and combine all the sauce ingredients (except the cornstarch and water for the slurry) in a small bowl.
In a separate small bowl, stir the cornstarch and water until smooth to make the slurry.
Heat oil in a wok over medium-high heat. Stir-fry the chicken until nearly cooked through, then remove from the wok.
Add garlic and ginger to the wok and stir-fry just until fragrant.
Add the snow peas, mushrooms, carrots, bamboo shoots, and water chestnuts. Stir-fry until the snow peas turn bright green.
Pour in the sauce and bring to a boil.
Stir in the cornstarch slurry and let the sauce thicken slightly.
Return the chicken to the wok and toss everything together until well combined and heated through.
Serve hot with steamed rice or your favorite sides.
Notes
Vegetable swaps: Snow peas can be substituted with snap peas or green beans; mushrooms can be swapped for shiitake, oyster, or canned straw mushrooms. Thinly sliced celery or cabbage stems work well in place of bamboo shoots.Make ahead: You can prep the sauce, chop the vegetables, and marinate the chicken ahead of time. Store everything separately in the fridge and stir-fry just before serving.