Brown the ground beef with the green peppers, onion, most of the garlic, nutmeg, red pepper flakes, salt and pepper. When it's done, drain any excess grease off.
Add the chopped mushrooms and cook 5 minutes, stirring. Add the wine, bring to a simmer and cook a minute or so, then stir in the beef broth, tomatoes, Worcestershire, and ketchup. Simmer for 10 to 15 minutes, until most of the liquid is evaporated. Stir now and then.
Meanwhile, mix some of the garlic with some softened butter, enough to spread over however many rolls you are using. Broil the buns a bit until browned slightly. Place some of the meat on top of each bun and top with a slice of mozzarella cheese. Broil until the cheese is softened and serve.