Preheat an outdoor grill for high heat and lightly oil the grate. Set a cast iron flat-top griddle or large cast iron skillet onto the grill and preheat until smoking.

Spread butter on the inside of the buns and toast on the flat-top until lightly browned. Set aside.

Form meat into 8 loosely-packed balls, 2 ounces each. Place each ball on the hot flat-top, cover with parchment, and smash down to a 1/4 inch thickness using sturdy spatulas or the bottom of a small skillet. Sprinkle the meat with salt.

Grill for about 45 seconds, until the edges are dark brown and the centers are light pink. Flip over, cover 4 patties with cheese, and grill an additional 15-20 seconds. Stack plain patties over the cheese-covered patties to form 4 stacks.