Divide your fresh ground beef into four equal portions on a clean surface. Shape each chunk gently with your hands into a round disc about 4 inches wide and 1 inch thick. Do not overwork the meat or pack it tightly because that makes the final texture tough and dense. Press a small indentation into the center of each patty using your thumb. (I tried skipping the thumbprint the first time, the burgers puffed up into round footballs that rolled right off the buns. This indent is the golden trick.) Keep the edges slightly irregular and natural rather than perfectly smooth. Make sure the patties are even in thickness except for that central dimple. This ensures uniform heat distribution. Shape the beef gently, loose packing keeps the interior tender during cooking.

Place a large cast-iron skillet over medium heat (about 5 on a 10-dial) until the surface is hot. Spread a thin layer of unsalted butter directly onto the cut sides of your four split brioche buns. Place the buns cut-side down into the dry pan to catch the direct heat. Toast them for exactly 2 minutes without moving them so they develop an even surface. You will hear a gentle sizzling sound as the butter melts into the crumb. The edges will turn deep golden brown and a crisp protective crust will form across the entire cut face. Remove the buns immediately when you smell that rich toasted pastry aroma. Leaving them longer will blacken the sugar in the bread. Toast the bread first, the buttery barrier prevents the burger juices from making the bottom bun soggy.

Turn the stove up to medium-high heat until the cast-iron skillet is hot but not smoking. Season the top of each raw patty generously with fine sea salt and coarse black pepper right before cooking. Place the patties seasoned-side down into the hot pan with clear space between them. Sear the meat for exactly 3 minutes without moving or pressing them down with a spatula. (I used to press them with a spatula. The first squeeze leaks half the juice, don't do it.) You will hear a loud aggressive sizzle and notice the bottom edges turning completely opaque and dark brown. Flip the patties carefully once you see that deep color creeping a quarter of the way up the sides. Miss this window and the exterior chars before the inside warms. Sear 3 minutes without moving, the fond builds the crust later.

Flip the patties over using a sturdy metal spatula to expose the beautifully browned seared crust. Place one thick slice of sharp cheddar cheese directly onto the hot top of each cooked patty. Pour a single tablespoon of tap water into the empty spaces of the hot pan. Cover the skillet immediately with a lid or a large metal bowl to trap the rising steam. Let it cook on medium-high heat for exactly 1 minute until the cheese runs smooth. You will see the cheese drape unevenly over the irregular edges of the beef like a thick blanket. The cheese should look glossy and fully molten without separating into oil. Remove the pan from the heat source right away to stop the cooking process. Cover the pan with a lid, trapped steam melts the dairy instantly before the beef overcooks.