Preheat a large cast iron skillet over medium-high heat. Add the ground beef and cook until it forms a deep brown crust on the bottom, breaking it apart halfway through.

Remove the beef and leave the rendered fat in the skillet. Add the butter, diced onions, bell peppers, and minced mushrooms. Let them brown for 1-2 minutes undisturbed, then stir and let them brown for another 1-2 minutes.

Return the browned beef to the skillet. In a small cup, whisk the beef broth and cornstarch until smooth. Pour this mixture into the skillet with the ketchup, Worcestershire sauce, salt, and pepper, stirring everything together.

Cook the filling until it thickens and becomes slightly less liquidy, about 3-5 minutes.

Turn off the heat and stir in the chopped Provolone cheese until it melts into a gooey, delicious mixture.

Pile the cheesy filling high on toasted brioche buns, and enjoy this comforting meal!