In a medium bowl, combine the sliced chicken, water, oyster sauce, cornstarch, and vegetable oil. Massage the marinade ingredients until absorbed by the chicken, and set aside for 30 minutes to marinate.
Meanwhile, make the sauce mixture. Combine the sugar, salt, sesame oil, white pepper, and chicken stock, and set aside.
Bring 6 cups of water to a boil. Blanch the broccoli for 1-2 minutes, drain, and set aside. How long you cook your broccoli is a personal preference. If you like your broccoli crunchy, 1 minute is plenty of time. If you like your broccoli soft, for 2 minutes (or even a little longer), or until it is to your liking.
Let the water come back up to a boil. Add the chicken, and stir to separate the pieces. Cook just until the chicken turns opaque, and remove using a strainer. Set aside. Discard the water in the wok, and wash the wok clean.
Heat your wok over medium high heat until it's completely dry. Add the vegetable oil, ginger, and garlic. Cook for 20 seconds, and add the rice wine around the perimeter of the wok.
Next, stir up the warmed chicken stock and seasonings, and add it into the wok. Keep stirring for another minute to combine, and let everything come up to a simmer.
Mix the cornstarch and water together into a slurry. Pour the cornstarch slurry into the liquid slowly, stirring constantly, until thickened. Use only ¾ of the slurry, and check the thickness of the sauce. Add the rest if necessary. Or if the sauce is too thick, add more chicken stock or water.
Add the chicken and broccoli back to the wok, and stir it in for 30 seconds. Taste for seasoning, and adjust if needed. Serve immediately!