Preheat the broiler to high.
For the meat sauce, heat a deep skillet or a heavy-bottomed pot over medium-high heat with 2 tablespoons of EVOO, twice around the pan. Add the ground beef and cook until lightly browned, breaking up the meat with the back of a wooden spoon. Add green pepper, onion, 3/4 of the garlic, mushrooms, allspice, red pepper flakes and a little salt and pepper to the beef and cook for about 5-8 minutes.
Add the wine and cook another minute then add the beef stock, Worcestershie and tomatoes. Bring the mixture up to a bubble, reduce the heat to medium-low and gently simmer for 10 minutes. Finish it by stirring in a handful of chopped parsley.
While the meat is simmering, combine the remaining garlic with the soft butter, basil, parmesan cheese and a little salt and pepper in a mixing bowl. Split the rolls in half lengthwise without cutting all the way through and separating the halves. Press open the rolls by flattening them out a little bit. Slather the insides with the butter and place 2 slices of the mozzarella on each roll. Toast until golden brown under the broiler, about 2-3 minutes.
Top one side of the cheesy garlic rolls with a heap of meat and get prepared to get sloppy with Messy Giuseppe!