
Mix the melted butter, Worcestershire sauce, fish sauce, and smoked paprika in a small bowl to create the smash burger sauce.
In a larger bowl, combine the ground beef with the smash burger sauce, mixing well with your hands. Form the mixture into 4 balls and refrigerate for 20-30 minutes.
Butter the brioche buns and toast them on a skillet or griddle until golden brown.
Prepare the house sauce by mixing mayo, ketchup, horseradish, Worcestershire, sriracha, paprika, and minced shallot. Season with salt to taste.
Heat a cast iron skillet or flat griddle until very hot. Place the beef balls on the hot surface, sprinkle with salt, and let them sizzle for about 20 seconds.
Place a piece of parchment paper on each burger and press down with a heavy, flat tool to flatten them into thin patties. Cook for a few minutes, then flip and top with cheese.
Allow the cheese to melt and the patties to brown on the other side for 1-2 minutes. Assemble the burgers with toasted buns, patties, cheese, lettuce, tomato, onion, pickle slices, and a generous smear of house sauce.