Combine tomato juice, oil, basil, oregano, pepper, and garlic. Set aside.
Steak and onions:
Trim fat from steak and cut steak into four equal portions. Place meat in a plastic bag set in a deep bowl. Pour marinade over steak. Seal bag; turn to coat steak well. Marinate overnight in the refrigerator. Then, drain steak, reserving marinade.
Place onions on an 18-inch square of heavy foil. Turn edges of foil up slightly. Drizzle 1/2 cup of the reserved marinade over onions. Fold foil tightly to seal. Grill onion packet and steak on an uncovered grill directly over medium coals for 10 minutes. Turn onion packet and steak; brush steak with marinade. Discard any remaining marinade. Grill steak to desired doneness, allowing 8 to 10 minutes more for medium doneness. Grill onions 8 minutes more or until tender.
Unwrap onions and place on a serving plate. Arrange meat atop onion. Spoon any remaining sauce from onions over the meat. Serve with steamed green beans, if desired. Makes 4 servings.