Bolognese-Style Sloppy Joes

Heat oil in a large skillet over medium-high; add sausage, and cook, stirring often to break up sausage, 5 minutes. Add onion, bell pepper, carrot, and garlic, and cook, stirring often, until sausage is cooked through and vegetables are very soft, 7 to 8 minutes.

Add wine, and cook over medium-high, stirring often, until liquid has evaporated. Stir in crushed tomatoes, brown sugar, Worcestershire sauce, salt, and crushed red pepper. Bring to a boil; reduce heat to low, and simmer 15 minutes. Spoon about 2/3 cup sausage mixture over bottom half of each focaccia piece, and, if desired, sprinkle with Parmigiano-Reggiano. Cover with top focaccia pieces.