Heat a cast iron skillet over medium-high heat. Add the ground beef and let it sit undisturbed for 3–4 minutes.

In the same skillet, melt the butter over medium heat, then add the chopped onions, bell peppers, and mushrooms. Cook for 5–6 minutes until softened.

Return the browned beef to the skillet. Whisk together the beef broth and cornstarch, then add along with ketchup, Worcestershire sauce, salt, and pepper. Simmer for 3–5 minutes.

Turn off the heat. Stir in the provolone cheese until melted and creamy.

Spoon the mixture onto toasted brioche buns and serve warm.