In a skillet, cook ground beef over medium heat until browned.
Add diced onion and bell pepper; sauté until soft.
Stir in minced garlic and cook for 1 minute.
Pour in beef broth and Worcestershire sauce.
Add mustard, salt, and pepper; mix well.
Let the mixture simmer for 10 minutes, stirring occasionally.
Once thickened, remove from heat and stir in shredded cheese.
Toast hamburger buns lightly in another skillet.
Fill each bun with the beef mixture generously.
Serve warm with your favorite sides.