In a large cast iron skillet over medium-high heat, cook the ground beef undisturbed until a deep brown crust forms. Break apart and continue cooking until fully browned and 160°F.

Remove the beef from the skillet, leaving the fat. Add butter, then onion, bell pepper, and mushrooms. Sauté without stirring for 1-2 minutes, then stir and cook until caramelized.

Return the beef to the skillet. Add ketchup, Worcestershire sauce, salt, and pepper. In a small cup, mix beef broth and cornstarch; add to skillet and stir until sauce thickens, about 3-5 minutes.

Turn off the heat and fold in the chopped Provolone cheese, stirring until melted and creamy.

Toast the brioche buns under a broiler or in a toaster oven. For added flavor, butter the insides of the buns before toasting.

Spoon the beef mixture generously onto the toasted buns. Serve warm and enjoy!