Preheat a large skillet over high heat for about 2 minutes. Add the ground beef and let it sear undisturbed for 1 minute, then break it up and continue browning for 3-4 minutes.

Remove the beef from the skillet. In the same skillet, melt 2 tablespoons of butter and add the onions, bell pepper, and mushrooms. Cook for 5-7 minutes until tender.

Prepare the sauce by mixing beef broth, cornstarch, ketchup, and Worcestershire sauce in a bowl. Pour into the skillet with the vegetables and simmer for 3-5 minutes.

Return the browned ground beef to the skillet and cook for another 2 minutes, adjusting seasoning as necessary.

Remove from heat and stir in the provolone cheese until melted.

Butter the insides of the brioche buns and toast in a separate skillet for 2-3 minutes until golden brown.

Fill each toasted bun with the cheesy beef mixture and serve immediately.