Trim fat from around beef. Slice against the grain as thinly as possible. Marinate beef with soy sauce, Shao Hsing cooking wine, black pepper, cornstarch, and sesame oil for at least 30 minutes in the refrigerator.
Heat a wok or large pan with 1 tablespoon vegetable oil. Add red and green bell peppers and stir-fry for 2 minutes. Remove and set aside.
Add remaining oil into the pan. Fry ginger for about a minute, then add garlic and fry for another 30 seconds.
Add beef by spreading it out in the pan. Fry for about 3 minutes.
Return cooked red and green bell peppers to the pan. Stir to get everything well mixed. This takes about 2 minutes.