Heat a sauté 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. If there's excess grease in the pan, drain it out at this time.
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. Cook for about a minute.
Add cornstarch and stir until dissolved, about a minute. This thickens the beef broth to 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.
