Warm the olive oil in a large frying pan set over medium heat. Add the minced onion and chopped bell pepper, cooking for 4 to 5 minutes or until they soften and become aromatic.
Introduce the ground beef into the skillet, breaking it into small crumbles with a spatula. Continue to cook until browned all over and no longer pink. Drain off any surplus fat.
Incorporate the beef broth, Worcestershire sauce, ketchup, garlic powder, and season with salt and pepper to taste. Allow the mixture to simmer gently for 5 to 7 minutes until it slightly thickens and the flavors blend.
Reduce the heat to low and add the shredded provolone cheese. Stir thoroughly until the cheese has melted and the mixture becomes creamy and uniform.
(Optional) If desired, melt a bit of butter in a separate skillet and lightly toast the hamburger buns until golden and crisp.
Spoon generous scoops of the hot, cheesy beef filling onto the prepared buns. Serve promptly while still warm and melty.
Notes
Toasting the buns is optional but enhances texture and adds a rich buttery note to each bite.