Cut beef with grain into 2" strips. Slice beef across grain into thin slices. Toss beef with 1 teaspoon cornstarch, sugar, 1 tablespoon soy sauce and pepper, cover and refrigerate for 20 minutes.
Combine 1/2 cup chicken broth, oyster sauce, remaining soy sauce and cornstarch, set aside.
Heat wok, add 1 tablespoon oil and rotate to coat inside. Add beef, garlic and ginger and stir fry until beef is brown, about 3 minutes. Remove from wok.
Add 1 tablespoon oil to wok, add broccoli, onions and mushrooms, stir fry 3-4 minutes. Stir in 1/4 cup chicken broth and beef and heat to boiling. Stir in cornstarch mixture, cook and stir until thickened, about 1 minute. Serve with steamed rice.