Heat a cast iron skillet over medium-high heat, allowing it to get nice and hot. Add your ground beef to the skillet, spreading it into an even layer without stirring for about 3-4 minutes.

Once the ground beef is beautifully browned, carefully remove it from the skillet and set it aside on a plate.

In the same skillet, melt a couple tablespoons of butter over medium heat. Add diced onions, bell peppers, and mushrooms. Sauté undisturbed for about 1-2 minutes, then stir and continue cooking until softened, roughly 3-5 minutes.

Return the browned beef to the skillet with the sautéed vegetables. In a separate bowl, whisk together the beef broth and cornstarch until smooth, then pour this mixture into the skillet. Add in the ketchup, Worcestershire sauce, salt, and pepper.

Stir the mixture well and bring it to a gentle simmer over medium heat. Allow it to cook for about 3-5 minutes, stirring occasionally, until the sauce thickens.

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

Toast your brioche buns in the same skillet or in a toaster until golden, then spoon the thick, cheesy beef mixture onto the warm buns.