In a medium bowl, mash together blue cheese and butter. Salt and pepper mixture, to taste. Place mixture on plastic wrap and roll up to form a cylinder. Refrigerate until firm, about 1 hour. After cheese mixture has firmed up, divide ground beef into 4 equal portions and make an indention in the center of each patty. Slice blue cheese mixture into 4 equal parts and place in indentation in patties. Mold ground beef around the cheese mixture to cover. Cook on hot grill or in skillet to desired doneness.
Recipe courtesy of Paula Deen