Thinly slice your chicken breast against the grain (it’s easier when the chicken is partially frozen). Combine the sliced chicken with the water, cornstarch, vegetable oil, and oyster sauce. Massage the marinade ingredients into the chicken until there is no standing liquid. Set aside for 15-20 minutes while you prepare your other ingredients.
After washing, trim the ends off the Chinese broccoli, and tear the stalks into smaller pieces (separate individual leaves, and snap stems in half). Roughly tear the oyster mushrooms and set aside. If using shiitake mushrooms, slice them. Also prepare your ginger and garlic.
In a measuring cup or small bowl, combine the chicken stock, light soy sauce, oyster sauce, white pepper, sugar, and sesame oil. Set aside.
Meanwhile, bring a wok or pot of water to a boil with 1 tablespoon of vegetable oil. Once at a rolling boil, add the greens and blanch for 30-45 seconds. Quickly remove from the wok with a strainer or slotted spoon, and make sure to drain well of any excess liquid.
Heat a clean, dry wok over high heat until it starts to smoke. Add 1 tablespoon of oil to the wok, spreading it around to coat the surface. Add the chicken pieces in one layer, and allow it to sear on one side for 20-30 seconds. Flip, and sear on the other side for 20-30 seconds. Stir-fry for another 10-15 seconds, and remove the chicken from the wok. Set aside.
Lower the heat to medium low, and add another tablespoon of oil to the wok, along with the ginger. Cook for 1 minute. Turn up the heat to high, and add 2 tablespoons of water to deglaze the wok, along with the mushrooms and garlic. Stir-fry over high heat for 1 minute, and add the Shaoxing wine. Stir-fry for 1 more minute.
Stir in the sauce mixture and bring to a simmer. Quickly mix 2 teaspoons of cornstarch with 1 tablespoon of water, and pour the mixture into the sauce. Cook for 15 seconds, until the sauce has thickened.
Stir the chicken into the thickened sauce, and then add the blanched greens. Stir-fry for another 30 seconds, until everything is combined and coated in the sauce. Serve immediately.