To make the special sauce: Combine the mayo, ketchup, chopped pickles, sugar, white vinegar, and salt and pepper. Set aside in the refrigerator until ready to use.
To make the caramelized onions: Heat 1 TBSP of oil in a skillet over medium low heat. Add the onions, and 1/2 tsp salt. Stir. Cook, stirring occasionally, for about 15-20 minutes, or until golden brown and caramelized. Add 1 TBSP water at a time, waiting for it to evaporate before adding next TBSP. Keep warm.
Divide the ground beef into 8 balls. Place on a large sheet of parchment paper, leaving 2-3 inches in between each ball. Place another sheet of parchment on top.
Using a heavy pot or press, press the balls into thin rounds. Cut squares around the patties, and stack on a plate.
Melt the 4 TBSP of butter in a large skillet. Toast the buns, cut side down in the pan for 2-3 minutes, or until golden brown. Set aside.
Heat oil in the same pan. Flip 2 patties into the pan at a time, removing parchment paper. Brush the top with mustard, and sprinkle with salt and pepper.
Cook 2-3 minutes, and flip. Cook an additional minute, and top each patty with a slice of cheese and scoop of onions. Stack the patties together.
To assemble burgers, spread the sauce on the top and bottom of the buns. Add lettuce, tomato, pickles, and then double burger patties. Serve with some crispy fries!
