Make the sauce! Combine the ingredients (mayonnaise, ketchup, mustard, pickles, garlic powder, paprika, and cayenne) in a food processor or blender until smooth.
Make the patties! Very carefully mix together the sirloin, chuck, and brisket in a bowl until just combined. Form into 4 even patties. They should be about about 2 inches tall and 2 1/2 inches wide. The goal is to get them pretty thin, but remember they flatten out as they cook.
Prep your buns! Split open the potato buns and spread the inside with a thin coating of melted butter. Place them buttered side down in a skillet until brown, about 1 minute.
Add oil to a large, heavy-bottomed skillet over medium-high heat until it just starts to smoke (you can use a regular pan, but a heavy bottom skillet is better). Also, you’ll notice that there isn’t much oil. This is on purpose and one of the tricks to getting the perfect burger.
Season beef patties on top side with salt and pepper, then transfer to the pan with the seasoned side down. After you put the burger in the pan, use a spatula and press down and lightly flatten the beef patties. Season the top side with salt and pepper and cook until a crisp brown crust has formed (about 2 minutes).
Carefully flip the burger over over. Top each patty with 1 slice of American cheese and cook until the cheese has melted (another minute). Transfer patties to your bun and top with the 1 leaf of lettuce, 2 tomato slices and 1 tablespoon of fake shack sauce.