If you want to make ‘special sauce’, whisk together mayonnaise, ketchup, garlic powder, and Worcestershire sauce. Set aside.
Divide beef into 4 even portions (these will be 4 oz each - no need to weight them, but just in case you wanted to) on a large sheet pan. Use your palm to gently press down on each portion so it is about 1/2 -inch thick. Season the beef on both sides with salt and pepper.
Heat a large griddle to medium heat. Add butter, moving it all around on the griddle as it melts.
Add burger patties and use a sturdy flat spatula to press very firmly down on the burgers until the patties are slightly larger than your burger buns. The edges should be uneven (craggy edges will get nicely browned).
Cook the burgers, without moving them, until light brown, 2 to 3 minutes. Flip burgers and top with cheese. Cook until cheese is melted, 1 to 2 minutes more.
Toast buns, if you’d like. (Note: I find that with really soft burger buns, they are sometimes better untoasted because it really highlights the golden crispness of the burger patties.)
Spread sauce over inside of buns. Fill with burger patties and any toppings you’d like. Enjoy with fries!