Heat butter or oil in a large skillet over medium-high heat. Add the ground beef, onions and bell peppers. Cook, breaking up the beef, for 6-8 minutes until the beef is browned and the vegetables are soft. Drain excess grease.

Add the ketchup, steak sauce, Worcestershire sauce and seasonings. Stir and cook for 2-3 minutes to flavor the meat.

In a small bowl, whisk cornstarch into beef broth until smooth and pour into the skillet. Bring the mixture to a simmer and cook for 5-7 minutes, stirring occasionally, until the sauce is thick and glossy.

Turn off the heat and stir in 1 cup shredded provolone cheese. Cover with a lid for 30-60 seconds, then stir again until it is incorporated. The cheese will be stringy at first, but it will melt beautifully after a couple of minutes.

Meanwhile, place the tops of buns on a baking sheet. Add 1 slice of provolone cheese to each. Broil in the oven for 1-2 minutes until the cheese is melty.

Pile the meat mixture onto the bottom buns, add the top buns, and serve immediately.