In a small bowl, whisk together mayonnaise, ketchup, mustard, pickle relish, and garlic powder to make the sauce. Refrigerate until ready to use.
Divide ground beef into 4 equal portions and loosely roll into balls.
Heat a cast-iron skillet or flat griddle over high heat until very hot.
Place beef balls onto the hot surface and smash thin using a sturdy spatula or burger press.
Season with salt and pepper immediately.
Cook for 2–3 minutes until crispy edges form.
Flip burgers, top with cheese, and cook another 1–2 minutes until cheese melts.
Toast buns lightly on the skillet.
Assemble burgers with sauce, patties, and desired toppings.
Serve immediately while hot and juicy.