Place beef chunks in a single layer on a baking sheet with half inch in between. Place in freezer for 25 minutes.
Coarse ground the meat in food processor at 10 to 15 second pulses. Stop and redistribute the meat around the bow if necessary to make sure it is evenly ground. Dump onto baking sheet and spread over sheet, while discarding large pieces of hard meat or fat.
Gently separate ground meat into 4 equal mounds. Shape each mound with your fingers into loose patty 1/2 inch thick and 4 inches in diameter. Season each with salt and pepper. Flip with spatula and season the other side. Refrigerate for 10 minutes.
Add butter to a large cast iron skillet over high heat. Cook each patty for 3 minutes, flipping with a spatula, cook for 1 minute. Add cheese to the top and cook for an additional minute. Remove and serve with garnish.