For these burgers, Martha loves Milton Creamery's Prairie Breeze cheddar and Challerhocker Swiss, both available at Murray's Cheese. Grate the horseradish and add it to the cheeses right before grilling; it quickly loses its potency once grated.
Preheat grill to medium. Combine both cheeses and horseradish. Gently form beef into 8 patties, each about 4 inches in diameter. Season generously with salt and pepper. Brush grates with oil; grill burgers 4 minutes. Flip; top each with just over 1/4 cup cheese mixture. Cover grill and cook, about 4 minutes more for medium-rare. Remove burgers from grill; let rest 5 minutes before assembling.
Combine mayonnaise and ketchup. Brush split sides of buns with butter; grill until lightly toasted. Season tomato with salt and pepper. Sandwich burgers in buns with mayonnaise mixture, tomato, bacon, lettuce, and pickles.