Apple and Onion Cheddar Burgers

1 1/2 cup apple butter, divided
2 tablespoons Worcestershire sauce
1 teaspoon salt
1/4 teaspoon pepper
1 1/4 pound ground chuck
1 large Golden Delicious apple, sliced into 1/2 inch rings
1 large white onion, sliced into 1/4 inch rings
non-stick cooking spray
4 slices cheddar cheese, sliced thick
4 kaiser rolls

In a large bowl stir 1/2 cup of the apple butter, Worcestershire sauce, salt and pepper together well. Crumble the uncooked ground chuck into the bowl with the apple butter mixture. Coat the meat well. Shape 4 burgers. Brush the apple and onion slices with the remaining apple butter. Spray the grill grate with the butter non stick cooking spray. Heat the grill to medium high heat. Place the burgers, apples and onions on the grill and cover. Grill about 5 minutes per side. When done the meat will no longer be pink and the apples and onions should be tender. Remove the apples and onions. Place a slice of cheddar on the top of each burger. Recover and cook an additional 1 minute. Remove the patties. Lightly coat the inside of the rolls with the cooking spray. Cook on the grill for about 1 minute to toast. Remove. Place a burger on each roll and top with the apple and onion slices.