Mix mayonnaise, ketchup, mustard, white wine vinegar, relish, garlic powder, onion powder, smoked paprika, and sugar. Stir until combined. Refrigerate.
Divide cold ground beef into 8 equal balls (87g each). Roll loosely. Do not overwork.
Heat a cast iron skillet over high for 3 to 4 minutes until smoking. Add oil.
Place 2 beef balls in the pan. Immediately press each one through a parchment paper square with a flat metal spatula for 10 seconds until 1/4 inch (6mm) thin. Season tops with salt and pepper.
Cook undisturbed for 2 minutes until edges are fully browned.
Flip with a thin spatula, scraping firmly under the crust. Cook the second side for 1 minute. Place 1 slice of American cheese on each patty. Cook 30 seconds until cheese melts.
Stack one patty directly on top of the other in the pan. Press gently for 3 seconds. Remove. Repeat with remaining patties.
Toast bun halves face-down in a dry pan over medium heat for 60 to 90 seconds.
Spread sauce on both bun halves. Assemble: pickles, double patty stack, tomato, lettuce, sliced onion. Serve immediately.