Heat a large skillet over medium heat and add the ground beef. Cook for about 7-8 minutes, until beef is no longer pink, breaking it apart and stirring as it cooks. Once cooked through, remove the beef from the pan.
Keep beef fat in the skillet and add butter onion, bell pepper, and mushrooms. Cook them until tender, stirring occasionally.
Now add beef back to the pan and reheat over medium heat for 1-2 minutes, stirring often.
Sauce: In the small bowl whisk together beef broth, Worcestershire sauce, ketchup and Dijon mustard. Add sea salt, pepper, garlic powder and onion powder. Pour sauce ingredients into the skillet with beef and veggies, and stir until evenly coated.
Keep the heat on until the sauce with beef starts bubbling up, about 2-3 minutes. Then add sliced Provolone cheese on top of the beef in the skillet. Next sprinkle with Cheddar cheese. This step needs to be done right when Sloppy Joes are ready to be served.
To serve: Serve the sloppy joe mixture on buns of your choice.