In a small bowl, stir together the grated cheese with the mayonnaise, pimentos, grated onion, and Worcestershire sauce. Sprinkle with salt and pepper. Set aside.
Prepare a medium-hot charcoal fire or heat a gas grill to medium-high. Set the burgers on the grill, and cook, flipping only once, until they reach desired level of doneness. For medium-rare, it will take 9-10 minutes. Spoon 2 tablespoons of the pimento-cheese mixture on each burger during the last minute or so of cooking. Cover, and allow to melt.
Serve on buns with lettuce and tomato. Enjoy!