1In shallow glass or plastic dish or heavy-duty resealable plastic food-storage bag, mix honey, gingerroot, soy sauce and beer. Add beef; turn to coat with marinade. Cover dish or seal bag and refrigerate, turning occasionally, at least 4 hours but no longer than 24 hours.
2Heat coals or gas grill for direct heat. Remove beef from marinade; reserve marinade. Cover and grill beef over from medium heat about 12 minutes for medium doneness, turning after 6 minutes and brushing frequently with marinade. Discard any remaining marinade.
3Cut beef into thin slices. Serve beef in pita fold breads with tomato and onion.