Heat a cast iron skillet over medium-high heat. Add the ground beef and let it sear without stirring for about 3–4 minutes until it forms a deep brown crust.

Once about half of the beef is caramelized, remove it from the skillet and set it aside on a plate.

In the same skillet, melt 1 tablespoon of butter over medium heat. Add the chopped onions, bell pepper, and mushrooms, stirring occasionally until they’re soft and golden.

Return the browned ground beef to the skillet, mixing it in with the sautéed vegetables.

In a small bowl, whisk together 1 cup of beef broth and 1 tablespoon of cornstarch until smooth. Pour this mixture into the skillet along with ½ cup of ketchup, 1 tablespoon of Worcestershire sauce, salt, and pepper.

Turn off the heat and stir in 1 cup of chopped provolone cheese until it melts into a creamy consistency.

Spoon the hot beef and cheese mixture generously onto toasted brioche buns and serve while hot.