To prepare steak, trim fat. Cut steak diagonally across grain into thin slices. Combine 1 tablespoon sugar, 2 tablespoons soy sauce, 1 1/2 tablespoons vinegar, and 4 garlic cloves in a large zip-top bag. Add steak; seal and marinate in refrigerator 1 hour, turning bag occasionally. Remove steak from bag; discard marinade.
To prepare sauce, combine 1/2 cup soy sauce, water, and next 6 ingredients (water through broth); stir with a whisk.
To prepare vegetables, heat 1 1/2 teaspoons vegetable oil in a large nonstick skillet over medium-high heat. Add steak; cook 7 minutes or until steak loses its pink color. Remove steak with a slotted spoon; set aside. Wipe pan clean with a paper towel. Heat 1 1/2 teaspoons oil in pan. Add onions, ginger, and 2 garlic cloves; stir-fry 1 minute. Stir in sauce and bean sprouts; bring to a boil. Cook 1 minute. Stir in steak and noodles; toss well.