Brown ground beef in skillet over medium heat. Once the hamburger is about half cooked, add in the diced onions and green peppers. Cook until beef is cooked through. Drain excess fat if needed.
In a measuring cup, combine the beef broth and corn starch until dissolved. Add mixture to ground beef. Add ketchup, Worcestershire, salt and pepper. Cook over med-high heat until the liquid thickens and reduces, about 3-5 minutes.
Reduce heat to low and add in chopped provolone cheese. Stir until melted.
Butter the hamburger rolls or sub rolls with butter or margarine, and place under the broiler until golden and crisp. Watch closely so they do not burn, it only takes a couple minutes! Assemble and enjoy!
Additions I have made are a few dashes of garlic powder and seasoned salt, because why not?
If they seem to need more liquid add a splash of beef stock. If they seem a little too sloppy, make a little more cornstarch-beef stock slurry and bring to a simmer to thicken. If they are still too sloppy...tough, they are sloppy joes.
I have served these on toasted wheat rolls and also on toasted King's Hawaiian hot dog rolls (pictured) which worked great! The hot dog rolls are sliced on top so they really hold up nicely to the sloppiness of the sandwich.