Mix all ShackSauce ingredients. Refrigerate at least 10 minutes. Form beef into loose 3-oz balls. Season with salt and pepper just before cooking.
Heat cast iron over high heat until smoking. Smash beef balls thin. Cook 90 seconds undisturbed until edges brown.
Flip once. Add cheese immediately. Cook 45 more seconds until cheese is fully melted.
Toast buns in pan drippings. Spread ShackSauce on both halves. Stack patties, add cold lettuce and tomato. Serve immediately.
Notes
ShackSauce improves after 24 hours in the fridge. Let beef sit at room temperature 10 minutes before cooking. Build burgers to order if serving a crowd — don't pre-assemble.