Preheat grill or a cast iron skillet to high.
Divide the beef into 8 (4-ounce) burgers. Season on both sides with salt and pepper, to taste. Grill or cook in the skillet for 3 to 4 minutes on each side for medium-rare doneness. During last minutes of cooking add 2 slices of cheese to each burger, cover grill and let melt, approximately 1 minute. Place burger on bun and top with Horseradish Mustard, lettuce, Grilled Vidalia Onions, pickles and ketchup.
Whisk mustard and horseradish together in a small bowl.
Brush olive oil on both sides of the onions and season with salt and pepper. Grill the onion slices for 3 to 4 minutes on each side until golden brown.