Combine first 6 ingredients; stir until well-blended, and set aside.
Trim fat from steak. Cut steak diagonally across the grain into 1-inch-thick slices. Cut slices into thin strips. Combine steak, 1 tablespoon cornstarch, 2 tablespoons water, 1 tablespoon soy sauce, and 2 teaspoons sugar in a medium bowl; stir until well-blended. Cover and marinate in refrigerator 15 minutes.
Heat 2 teaspoons oil in a wok or large nonstick skillet over high heat. Add steak mixture; stir-fry 2 minutes. Remove steak from pan; set aside. Add remaining 1 teaspoon oil, green onions, and gingerroot; stir-fry over medium-high heat 30 seconds. Stir in broccoli and 1/4 cup water; cover and cook 3 minutes. Return steak to pan, and stir in oyster sauce mixture; stir-fry 2 minutes or until thick and bubbly. Serve over rice.