In a small bowl, combine ½ cup mayonnaise, 2 tablespoons ketchup, 1 tablespoon yellow mustard, 2 tablespoons finely chopped dill pickles, 1 teaspoon pickle juice, ½ teaspoon garlic powder, and ½ teaspoon paprika. Stir well and refrigerate until ready to use.

Divide the 1 pound ground beef into 8 equal portions and loosely roll into balls. Do not overwork the meat.

Heat a large cast iron skillet or griddle over high heat until very hot.

Place 2 to 3 beef balls onto the hot surface. Using a spatula, firmly smash each ball down into a thin patty.

Season the patties with some of the 1 teaspoon salt and 1 teaspoon black pepper.

Cook for about 2 minutes, until the edges are crispy and browned.

Flip the patties and immediately place 1 slice cheddar cheese over one patty in each pair. Cook for another 1 minute.

Stack a plain patty over a cheese topped patty to create 4 double burgers.

Lightly butter the 4 burger buns with 1 tablespoon butter and toast them in the pan until golden.

Spread a generous amount of the special sauce on both the top and bottom buns.

Add the burger patties, then top with ½ cup shredded lettuce, sliced onion, and pickle slices.

Close the burgers and serve immediately.