In a large microwave-safe bowl, add onions and bell peppers. Cook until softened, about 5 minutes.
In the meantime, in a large, nonstick pan add the beef. Cook until no longer pink. Be sure to break up the beef while browning. Drain fat.
Stir in softened onions and bell peppers, beef broth, steak sauce, ketchup, and Worcestershire. Season with ground pepper and garlic powder. Simmer until half of the liquid is absorbed, about 5 minutes.
Preheat oven to broil. Line a baking sheet with foil. Add the buns to a baking sheet. Open each side almost all the way but still keep the top and bottom of each bun somewhat attached. Spread over the top of each bun about ½ cup meat mixture. It won’t cover the entire bun. Cut each slice of cheese in half and lay the 2 halves on top of meat. Broil open-faced sandwiches until the bun is lightly toasted and the cheese is melted.
You can make as little as 1 or all 8 at once. Any leftover meat mixture freezes great. Pack in single or double serving size containers then freeze.
Serve with a fork and knife. It’s easier to eat that way.