Trim fat from around beef. Slice against the grain as thinly as possible. Marinate beef with soy sauce, Shao Hsing cooking wine, pepper, and cornstarch for at least 30 minutes in the refrigerator.
Heat 1 tablespoon vegetable oil in a wok or large pan. Add broccoli and red bell pepper. Stir-fry for about 3 minutes. Remove and set aside.
Add remaining 2 tablespoons vegetable oil to the pan. Fry ginger for 1 minute. Add garlic and fry for another 30 seconds. Add beef by spreading it out in the pan. Fry for 3 minutes.
Add ¼ cup (60ml) water followed by cooked broccoli and red bell pepper. Stir to get everything well mixed. This should take about 2 minutes.
Drizzle sesame oil over beef and vegetables, if using.
Remove and serve immediately with steamed rice.