Heat a saute pan over medium heat. Crumble ground beef and season with salt and pepper, then cook until browned, about 5 minutes. Remove from pan and set aside.
Add butter to pan. Once melted, add onion and bell pepper and saute until vegetables begin to brown and onions turn translucent, about 4-5 minutes.
Reduce heat to low, then return ground beef to pan. Add garlic powder, worcestershire sauce, and beef broth, scraping the bottom of the pan as you incorporate your ingredients.
Add cornstarch and stir until dissolved. This will thicken the beef broth and create a sauce. If beef looks dry, add 1-2 tablespoons of water.
Remove from heat. Top meat mixture with cheese slices and allow to set for 1-2 minutes, or until melted. Remove from heat, spoon onto rolls and serve immediately.
Want to spice things up? Try adding a dash of hot sauce or cayenne pepper to your sloppy joes. Or, dice a jalapeno and add with your onions and bell pepper.
If you're worried about your cornstarch clumping when adding it to the hot pan (I haven't experienced this issue but some readers have), feel free to whisk your broth and cornstarch in a separate bowl before adding them to the pan.
If adding mushrooms, add with the onions and bell pepper.
Leftovers will keep for 2-3 days in the refrigerator in a well sealed container.