Start by melting the butter in a large skillet over medium heat. Add the finely chopped onions and bell peppers. Sauté for about five minutes until they soften. Don’t rush this step; it helps develop the sweet flavor profile.

Next, toss in the finely minced mushrooms and continue to cook for another five to seven minutes. You'll notice the mushrooms will release some moisture. Stir occasionally; this combination creates a fantastic base for the sloppy joes.

Push the vegetables to the side of the skillet and add the ground beef. Break it up with a spatula and cook until browned, about 8 minutes. Make sure it’s well drained to avoid excess grease.

Now it’s time to build that irresistible sauce. In a small bowl, mix the beef stock, cornstarch, ketchup, Worcestershire sauce, garlic powder, salt, and black pepper. Pour this mixture into the skillet. Stir well, allowing the flavors to meld together.

Once the sauce is bubbling, sprinkle Provolone cheese over the meat mixture. Reduce the heat to low and cover the skillet for a few minutes. The cheese will melt into gooey goodness, integrating beautifully with the beef and vegetables.

Grab your brioche buns and spread a dash of Dijon mustard on the insides. Pile on the cheesesteak mixture. Close the buns and serve while hot, with sides that suit your taste.