Combine first 4 ingredients in a small bowl, stirring well. Set aside.
Cut steak diagonally across grain into thin slices (about 1/8 inch thick).
Add oil to preheated wok. Add steak, and stir-fry 6 minutes. Add ginger and garlic, and stir-fry 1 minute. Push steak to one side of wok. Add pepper and mushrooms; stir-fry 2 minutes or until crisp-tender. Add Sugar Snap peas and sesame seeds, and stir-fry 1 minute.
Stir soy sauce mixture, and add to wok, stirring constantly, until sauce is thickened and bubbly. Serve over rice.