Cut beef into 2x1/4-inch strips. Toss beef, 1 tablespoon vegetable oil, the cornstarch and 1/2 teaspoon soy sauce in glass or plastic bowl. Cover and refrigerate 20 minutes. Soak noodles in cold water 5 minutes; drain.
Heat wok or 12-inch skillet over medium-high heat until hot. Add 1 tablespoon vegetable oil; rotate skillet to coat side. Add gingerroot and garlic; stir-fry 30 seconds. Add vegetables; stir-fry until crisp-tender. Remove vegetables from wok.
Add 1 tablespoon vegetable oil to wok; rotate to coat side. Add beef; stir-fry until brown. Remove beef from wok.
Add broth, vinegar, honey, 3 tablespoons soy sauce and the red pepper to wok. Stir in noodles; heat to boiling. Cook over medium heat about 2 minutes, stirring frequently, until noodles are tender. Stir in beef, vegetables and onions; cook and stir 1 minute.