Blend together; the beef, Worcestershire sauce, salt, garlic salt, pepper. Add the eggs, mixing them in well. Form into 8 thin patties and set aside. Mix the mustard, onion, pickle relish and the cheese together and spread evenly on top of 4 of the patties, leaving a rim around the edges. Seal each of the covered patties with a plain patty and press the edges together to seal. Brush with melted butter and grill until desired doneness.