Heat the olive oil in a large skillet over medium heat. Add the ground beef and cook, breaking it apart with a spoon, until browned and no longer pink. Drain any excess fat if necessary.

To the skillet with the beef, add the chopped onion, green bell pepper, and minced garlic. Cook, stirring frequently, until the vegetables are softened, about 5-7 minutes. Season with salt and pepper.

Stir in the Worcestershire sauce, beef broth, and ketchup. Bring the mixture to a simmer and cook until slightly thickened, about 5 minutes. If you prefer a thicker sauce, stir in the cornstarch-water mixture and cook for an additional 2-3 minutes, or until the desired consistency is reached.

Reduce the heat to low. Lay the slices of provolone cheese over the top of the meat mixture in the skillet. Cover and let sit for a couple of minutes until the cheese is melted. Alternatively, you can stir the cheese into the meat mixture until it's evenly incorporated and melted.

Spoon the beef and cheese mixture onto the toasted hoagie rolls. Serve immediately.