For the special sauce: Stir together the mayonnaise, ketchup, mustard, relish and Worcestershire in a medium bowl. Set aside.
For the double cheeseburgers: Prepare a grill for cooking over medium-high heat.
Divide the ground beef into 12 equal portions. Roll each portion into a ball, then flatten it into a thin, 4-inch-diameter patty. Lightly sprinkle the patties with salt and pepper. Grill on one side until about halfway cooked, about 3 minutes. Flip the patties, sprinkle the other side with salt and pepper, top each with a slice of cheese and continue to cook until the patties are cooked through and the cheese has begun to melt, 1 to 2 minutes more.
Build each burger on a bun with 2 patties, tomato, lettuce, onion and a generous slathering of special sauce.