Divide the ground beef into 8 equal portions, about 56.7 g each. Gently roll each portion into a loose ball without overworking the meat. Chill the balls for at least 15 minutes.

Heat a large cast-iron skillet or griddle over medium-high heat until very hot. Add the butter and let it melt and shimmer.

Place 2 to 4 beef balls onto the hot skillet. Immediately use a sturdy metal spatula to press down firmly on each ball, smashing them into thin patties (about 1/4 inch thick). The goal is maximum surface contact.

Season the top of the smashed patties generously with salt and pepper. Cook undisturbed for 2 minutes, or until a deep brown crust forms on the bottom.

Flip the patties. Immediately top each patty with a slice of sharp cheddar cheese. Cook for another 1-1.5 minutes, until the cheese is melted and the second side is cooked through.

While the patties cook, lightly toast the cut sides of the brioche buns on the skillet.

Assemble the burgers: place two cheesy patties on the bottom half of each toasted bun. Top with the other half of the bun.

Serve immediately.