In a hot skillet, brown lean ground beef for about one minute undisturbed to develop a rich sear, then break apart and cook until fully browned. Remove from the pan and set aside.

In the same pan, melt butter, then add diced onions, bell peppers, and mushrooms. Sauté for about 5-7 minutes until browned and tender.

In a bowl, mix beef broth, cornstarch, ketchup, Worcestershire sauce, salt, and pepper. Pour over the sautéed vegetables and let it simmer for 3-5 minutes until thickened.

Return the browned beef to the pan, stirring to combine everything. Off the heat, gently mix in provolone cheese until melted.

Butter and toast the brioche buns in a skillet or oven until golden brown.

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