Cook the Beef and Vegetables:
Heat olive oil in a large skillet over medium heat. Add the ground beef, breaking it up with a wooden spoon, and cook until browned. Drain excess grease if necessary. Add the diced onion and bell pepper, cooking until softened (about 3–4 minutes).
Season the Mixture:
Stir in the garlic powder, Worcestershire sauce, and ketchup. Cook for 1–2 minutes to let the flavors blend.
Make the Sauce:
Sprinkle the flour over the beef mixture and stir well. Gradually add the beef broth while stirring to create a thick, saucy consistency. Reduce heat to low and simmer for 3–4 minutes.
Add the Cheese:
Stir in the shredded provolone cheese until melted and fully combined. Taste and season with salt and pepper as needed.
Assemble the Sloppy Joes:
Spoon the beef mixture onto the bottom halves of hamburger buns. Add the top buns to make sandwiches. Toast the buns beforehand for extra texture if desired.
Serve and Enjoy:
Serve warm with your favorite sides, such as fries, chips, or a fresh salad.