In a large skillet, cook ground beef over medium-high heat until brown.
Add onion and bell pepper, season with salt, and cook until veggies are softened, about 5-7 minutes.
Add garlic and cook one more minute.
Add Worcestershire, steak sauce, and beef broth.
Cook another 5 minutes, until beef broth has cooked down.
To make the cheese sauce:
In small saucepan, melt the butter.
Add the flour, and cook for 1 minute, stirring constantly.
Slowly add the milk, stirring constantly.
Bring milk mixture to a simmer, then add the shredded cheese.
Stir until cheese is melted. Remove from heat.
To assemble:
Place desired amount of beef mixture on buns, then top with cheese sauce.
Enjoy!