For marinade, combine 1/3 cup soy sauce, sherry, green onions, brown sugar, mustard, ginger, and garlic; mix well. Trim fat from steak. Place steak in a plastic bag set into a shallow dish. Add marinade; seal bag. Turn steak to coat well. Chill for 8 to 24 hours, turning steak occasionally. Remove steak from bag, reserving marinade.
Arrange preheated coals around a drip pan in a covered grill. Test for medium heat above pan. Place steak on grill over drip pan. Cover and grill for 28 to 30 minutes or until medium doneness, brushing occasionally with marinade up to the last 5 minutes of grilling. Remove steak from grill and cover it with foil. Cut into thin slices. Serve with additional soy sauce, if desired. Makes 6 to 8 servings.