Marinate the Chicken: In a bowl, combine the sliced chicken with water, oyster sauce, cornstarch, and vegetable oil. Mix thoroughly, ensuring the liquid is fully absorbed. Let it rest for 10 minutes.
Prepare the Sauce: In a separate bowl or measuring cup, blend the warm chicken stock with soy sauce, dark soy sauce, oyster sauce, sesame oil, sugar, and white pepper. Stir until fully incorporated and set aside.
Blanch the Broccoli: Bring a pot of water to a rolling boil and blanch the broccoli for 1 minute (or 2 minutes for a softer texture). Drain and set aside.
Cook the Chicken: Heat a wok over high heat until smoking. Add 2 tablespoons of vegetable oil and stir-fry the marinated chicken until it turns opaque, approximately 3 minutes. Remove from the wok and set aside; the chicken will finish cooking later.
Sauté the Aromatics: Without rinsing the wok, lower the heat to medium. Add the remaining tablespoon of vegetable oil, followed by the garlic and ginger. Stir for about 5 seconds until fragrant, then pour the Shaoxing wine along the perimeter of the wok. Immediately add the prepared sauce mixture and stir well to deglaze the wok. Let it simmer briefly.
Thicken the Sauce: Stir the cornstarch slurry and slowly incorporate it into the simmering sauce while stirring continuously. Allow the sauce to thicken to a smooth, glossy consistency, approximately 10–15 seconds.
Combine and Finish: Return the chicken and any accumulated juices to the wok, along with the blanched broccoli. Toss everything together until evenly coated in the thickened sauce.
Adjust and Serve: Customize the sauce as needed—add extra dark soy sauce for deeper color, more cornstarch slurry for a thicker consistency, or a bit of chicken stock if the sauce is too dense. Serve immediately with steamed rice.