In a small bowl, mix all of the ingredients together for the sauce and refrigerate until ready to use.
Heat a cast iron skillet or griddle over medium high heat until very hot; 3-5 minutes. Brush the skillet with half of the butter and add two portions of the beef.
With two spatulas or a grill press, smash the beef down into ½ inch thick patties, season with salt, and cook for 2 minutes.
Flip the patties, top them with slices of cheese and cook for an additional 1-2 minutes. Repeat with the remaining butter and beef.
Assemble the burgers. Spread the sauce on the top and bottom of each bun. Stack two patties on each bun followed by lettuce and pickle chips.