Preheat skillet to 325 degrees. Melt butter in skillet. Combine meat, green onions, parsley, garlic, egg, and breadcrumbs in a medium bowl. Form beef mixture into 4 patties. Add to skillet and brown on both sides, about 5 minutes per side. Add broth and tomato juice to skillet. Cook until beef is cooked through, about 5 minutes. Remove patties from skillet. Bring pan juices to a boil over high heat. Boil until reduced by half. Pour over patties.
Serves 4