1. Combine ground beef and pepper in a large bowl until blended. (Do not overwork meat mixture.) Shape mixture into 8 (4-inch) patties; spoon 1 1/2 Tbsp. pimiento cheese in center of each of 4 patties. Top with remaining 4 patties; pressing edges to seal. Cover and chill at least 30 minutes. Sprinkle evenly with salt.
2. Grill, covered with grill lid, over medium-high heat (350° to 400°) for 7 to 8 minutes on each side or until beef is no longer pink. Serve on buns with desired toppings and remaining pimiento cheese.