In a large skillet set over medium heat, add the ground beef and cook until browned (5-6 minutes)- Don’t forget to break it up into small pieces with the back of a wooden spoon.
Remove the ground beef from the skillet, keeping behind any rendered fat.
Add butter to the same skillet as well as the diced onions, bell peppers, and mushrooms. Allow the vegetables to slowly cook while stirring until they turn golden brown.
Put the beef back in the skillet with the vegetables.
In a small measuring cup, whisk the beef broth and cornstarch together until smooth. Add this mixture to your skillet, followed by the ketchup, Worcestershire sauce, salt, and pepper- Stir to combine.
Let the mixture simmer until it thickens, about 5 minutes. The mixture should still be a little saucy but not too liquidy.
Switch off the heat and stir in the Provolone cheese until it’s completely melted and creamy.
Spoon the saucy gooey meat mixture onto the brioche buns. Serve immediately with sides of your liking. Enjoy!