Stir together the mayonnaise, ketchup, sweet pickle relish, diced shallot and salt. Store in the refrigerator until ready to use.
FOR THE BURGERS
Shape the ground beef into four 6 ounce patties. Sprinkle the patties with salt and pepper. Cook on the grill for 3 minutes on each side, until you have reached desired doneness.
The last few minutes on the grill, place the sauerkraut on top of the burger. Place the cheese on top of the sauerkraut.
Serve with 1 tablespoon of burger sauce on toasted toasted rye bread.