Start by heating your large skillet over medium heat. Add the crumbled ground beef, sprinkle evenly with the salt and pepper, and cook for about 5 minutes until fully browned. Once cooked, remove the beef from the pan and set it aside on a plate; drain any excessive grease if necessary, but leaving a little bit adds flavor.
Add the butter to the now-empty pan and let it melt until it starts to bubble slightly. Toss in your diced onions and green bell peppers, sautéing them for 4-5 minutes until the onions become translucent and the peppers soften. You want the edges to get slightly golden brown to develop that rich, caramelized flavor base.
Turn the heat down to low and add the cooked beef back into the pan with the vegetables. Stir in the garlic powder, Worcestershire sauce, and beef broth, making sure to scrape up any browned bits from the bottom of the pan. Let this mixture simmer for about a minute to allow the flavors to meld together.
Sprinkle the cornstarch over the mixture and stir constantly for about one minute until the sauce thickens and becomes glossy. If the mixture seems too dry, you can splash in a tablespoon of water to loosen it up. Turn off the heat, lay the cheese slices directly on top of the meat mixture, and let it sit for a minute until melted before scooping onto your toasted buns.