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.