Divide the ground beef into 8 even portions and gently roll intoballs. Space the portions out on a piece of wax paper and topwith another piece of wax paper. Use your hand to firmly presseach ball into a flat, thin patty. Remove the top piece of waxpaper.
Finely chop two slices of cheese. Place a quarter of the choppedcheese in the center of four patties, leaving a border. Top each ofthe cheese-filled patties with a plain patty and use your fingers toseal the edges and press down to shape into large patties,ensuring that there are no holes in the patties. Place onparchment-lined tray and chill for 30 minutes.
While the burgers are chilling, place a heavy-bottomed skillet overmedium heat. Melt two tablespoons of butter in the skillet and thenadd the burger buns, cut side down, and cook for 2-3 minutes, untilgolden brown and toasted. Remove from the skillet and set aside.
Meanwhile, season both sides of the hamburger patties with saltand pepper. Melt a tablespoon of butter in the hot skillet and addtwo of the burger patties. Cook for 5-6 minutes, then flip and cookfor another 4-5 minutes, until evenly browned and cooked throughand the internal temperature reaches 160° F. Repeat with theremaining burgers. In the last minute of cooking, top burgers withadditional slices of cheese if desired.