Preheat the oven to broil. Bring a large pot of salted water to a boil and cook the fiori pasta until al dente. Set aside.
Heat olive oil in a large skillet over medium heat. Sauté onions and ground beef until the meat is browned. Add garlic and cook until fragrant. Stir in chopped vegetables and sauté until slightly softened.
Add canned tomatoes, oregano, basil, salt, and pepper. Cover and simmer for 20 minutes, stirring occasionally.
If using Béchamel sauce, melt butter in a small saucepan. Add flour and whisk until smooth. Gradually add milk, whisking constantly until the sauce thickens. Season with salt, pepper, and nutmeg.
Combine the cooked pasta and vegetable-meat sauce in a large mixing bowl. Stir in grated parmesan.
Transfer the mixture to a greased baking dish. Top with a layer of Béchamel sauce (optional) and grated mozzarella.
Broil for 2-3 minutes until the cheese is melted and golden brown. Serve hot.
Tip: Freeze mozzarella for 30 minutes before grating to make it easier to handle.