Form ground beef into two ¼-pound patties. Season with salt and pepper on both sides, to taste.
Grill patties on preheated grill until cooked through, or until desired doneness.
Meanwhile, layer each slice of cheese between two slices of Martin’s Butter Bread. Melt 1-2 tablespoons butter in a medium skillet or griddle. Grill sandwiches, in batches if necessary, flipping halfway through, until cheese is melted and bread is lightly toasted on both sides. Remove from skillet and set aside.
Assemble burgers by placing each patty between two grilled cheese sandwiches along with lettuce, tomatoes, and desired condiments such as ketchup and mustard. Serve.