Add the ground beef to a large cast iron skillet and brown on medium-high heat until a deep brown crust appears before breaking the beef apart.
Stir the ground beef and brown until a deep crust appears on about 50 or so percent of the beef.
Remove the beef and add the butter, onions, bell peppers, and mushrooms.
Let brown for 1-2 minutes before stirring, then let brown for another 1-2 minutes before stirring again.
Add the beef back into the pan.
In a small cup, mix the beef broth and cornstarch together.
Add the ketchup, Worcestershire sauce, salt, black pepper, and beef broth/cornstarch mixture into the pan.
Cook until the mixture is only slightly liquidy, about 3-5 minutes.
Turn off the heat, add in the provolone cheese, starting with half and then adding more until desired cheesiness is reached.
Serve on toasted brioche buns.