GRILL DIRECTIONS: Heat grill. In medium bowl, combine ground beef, blue cheese, parsley, salt and pepper; mix well. Shape mixture into 4 patties, 1/2 inch thick.
When ready to grill, place patties on gas grill over medium heat or on charcoal grill 4 to 6 inches from medium coals. Cook for 11 to 13 minutes or until patties are thoroughly cooked, turning once.
Meanwhile, heat oil in medium skillet. Add onion; cook and stir over medium heat for 3 to 5 minutes or until tender. Cook 15 to 20 minutes or until onions are golden and glazed, stirring frequently.
Place buns, cut side down, on grill. Cook 1 to 2 minutes or until buns are lightly toasted. Place patties and onions in buns.