Combine marinade ingredients in small bowl. Cover and refrigerate 1/2 cup marinade. Place beef steaks and remaining marinade in food-safe plastic bag; turn steaks to coat. Close bag securely and marinate in refrigerator 6 hours or overnight.
Remove steaks from marinade; discard marinade. Place steaks on grid over medium, ash-covered coals. Grill, covered, 12 to 14 minutes for medium rare doneness, turning once. (Do not overcook.)
Carve steaks into thin slices. Season with salt and pepper, as desired. Garnish with green onions, if desired. Serve with reserved marinade.