Preheat griddle or a cast iron skillet to high.
Divide the beef into 8 (115g) burgers. Season on both sides with salt and pepper, to taste. Griddle or cook in the pan 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 griddle and let melt, for approximately one minute.
Place burger on bun and top with horseradish mustard, lettuce, grilled vidalia onions, gherkins and tomato ketchup.
For the horseradish mustard: Whisk mustard and horseradish together in a small bowl.
For the grilled vidalia onions: Brush olive oil on both sides of the onions and season with salt and pepper. Griddle the onion slices for 3 to 4 minutes on each side until golden brown.