1. 1. Heat a large cast-iron or heavy skillet over medium–high. Add the ground beef and let it sear without moving it for a minute or two so the meat develops a flavorful, browned surface. Break the beef apart and continue cooking until roughly half the pieces show golden-brown edges — this adds depth to the final dish.

   2. Scoop the browned meat into a bowl, leaving the fat in the pan. Add the butter to the skillet, then toss in the chopped onion, bell pepper, and minced mushrooms. Give the vegetables a couple minutes undisturbed so they pick up color, then stir and cook another minute or two until they’re nicely caramelized.

   3. Return the beef to the skillet with the vegetables. In a small bowl, whisk together the beef broth and cornstarch until lump-free, then pour that into the pan. Stir in the ketchup, Worcestershire sauce, salt, and pepper, mixing so the sauce coats the meat evenly.

   4. Reduce heat slightly and simmer the mixture for 3–5 minutes, stirring occasionally, until the sauce thickens and clings to the beef. You want a hearty, spoonable texture rather than something runny.

   5. Remove the skillet from the heat and fold the chopped provolone into the hot mixture until it melts into a creamy, cheesy finish.

   6. Toast the brioche buns if you like (a quick buttered toast in a pan or under the broiler works great). Pile the cheesy beef mixture onto the buns and serve immediately.

Serve hot and expect deliciously messy bites — the perfect comfort-food mash-up for busy nights or casual get-togethers.