In a bowl, mix 6 tablespoons steak sauce, horseradish, parsley, and green onion. Form the ground beef into 4 patties. Brush the patties with the remaining steak sauce.
Place patties on the grill, and brush with the remaining steak sauce. Grill for 6 to 8 minutes per side, or until meat is no longer pink. Top with Muenster cheese and the horseradish sauce, and serve on buns.