Marinate the Chicken: In a bowl, combine the chicken with water, oyster sauce, and cornstarch. Add the vegetable oil, mixing well to coat the chicken.
Prepare the Sauce: In a small bowl, whisk together the chicken stock, sugar, soy sauce, dark soy sauce, oyster sauce, sesame oil, and white pepper. Set aside.
Blanch the Broccoli: Bring a pot of water to a boil and blanch the broccoli florets for 1-2 minutes, until bright green and slightly tender. Drain the broccoli and place in a bowl of cold water to stop the cooking. Set aside.
Sear the Chicken: Warm 1 tablespoon of vegetable oil in a wok or large skillet over medium-high heat. Working in batches, introduce the marinated chicken to the pan, cooking until it forms a beautiful golden-brown crust, which should take around 3 to 4 minutes. After achieving the desired color, transfer the chicken to a plate to keep it warm.
Sauté Garlic and Ginger: Pour in the remaining tablespoon of vegetable oil into the wok. Then, add the minced garlic and ginger, stir-frying for about 30 seconds until they become aromatic and release their delightful fragrance.
Add Broccoli and Chicken: Add the blanched broccoli and the seared chicken back into the pan. Pour in the Shaoxing wine and toss everything together thoroughly to combine the flavors.
Add Sauce and Slurry: Drizzle the prepared sauce over the chicken and broccoli, mixing well to ensure everything is evenly coated. Add the cornstarch slurry and stir until the sauce thickens and coats everything evenly.
Serve: Serve the Chicken and Broccoli with Brown Sauce hot, ideally with steamed rice. Enjoy!