Wash the broccoli and set aside. Make a slurry by mixing the cornstarch into the water and use a spoon to stir until completely dissolved. Mince the garlic.
Bring about 6 cups of water to a boil in your wok and add the broccoli. Blanch for a minute, drain, and put the broccoli into cold water to stop the cooking process.
Heat the wok over high heat. Once the wok is very hot, add the oil, garlic, broccoli, and wine. Stir fry for a minute and pour in the chicken stock. Let the mixture come to a boil, which should be quick since the heat is so high.
Add salt, white pepper, and sesame oil and give it another quick stir. Now make sure your cornstarch slurry is still well-mixed as the water tends to separate after some time. Stir in half of the slurry and let the sauce cook and thicken until it coats the back of a spoon. Add more slurry if it’s not thick enough. Plate and serve hot!
Chinese restaurants blanch the broccoli first because blanching cooks the broccoli faster and make the last step of stir frying and finishing much faster. The sauce also ends up cleaner in flavor. But you can also skip the blanching and cover your wok after adding the chicken stock (add a little extra stock or water to steam it). Then just let the broccoli steam in the covered wok for an extra few minutes, depending upon how crisp you like your broccoli.