Crumble ground beef into a large skillet set over medium high heat and cook until a brown crust forms on the beef crumbles.
Once cooked through, remove the beef from the pan, leaving any rendered fat behind.
Set the stovetop to medium heat and add onions, pepper, mushrooms, and butter to the skillet and cook until tender, stirring occasionally with a wooden spoon. Then add garlic and cook for an additional two minutes.
Return the ground beef to the pan, along with beef broth, ketchup, Worcestershire sauce, flour, salt, and black pepper. Stir to fully combine the meat mixture.
Bring the beef mixture to a simmer and cook until the liquid reduces to a thick saucy consistency. If it is too runny, continue cooking to thicken it further.
Lightly toast the insides of your hamburger buns, then add a large spoonful of the sloppy joe mixture, topping with a slice of cheese. Serve immediately.