Prepare your pimento cheese and refrigerate. Find the recipe here.
Preheat your grill or grill pan. Combine the ground beef, egg, and salt and black pepper in a large bowl. Mix together with clean hands and then form into thin patties (about 2 1/2 - 3 inches in diameter).
Grill your burgers to your liking, topping them with sliced cheese in the final minutes of grilling so that it melts. Remove from heat. At this time, you may also grill your burger buns by placing them directly on the grill with the inside face down. Grill until they are slightly charred.
In a small bowl, whisk together the ketchup, mayo and mustard. Spread a thin layer of the sauce on your burger buns. Top with a burger (or two), pimento cheese, and shredded lettuce.