Prepare barbecue (medium-high heat). Combine meat, onion, parsley, Worcestershire sauce, salt and pepper in medium bowl; blend well. Divide meat mixture into 2 equal portions. Shape each into ball. Poke deep hole in each ball and fill each with half of cheese. Mold meat around cheese to enclose. Flatten each filled burger to 3/4-inch-thick patty.
Grill burgers to desired doneness, about 5 minutes per side for medium. Grill muffin halves until beginning to color, about 1 minute per side. Serve burgers in muffins.