Lasagna Bolognese

Name: Lasagna Bolognese
Ingredients: 1 cup dried porcini mushrooms; 10 ounces white button mushrooms; 2 carrots, cut into 4 pieces; 2 stalks celery, cut into 4 pieces; 2 cloves garlic; 1 cup fresh parsley; 1 6-ounce piece prosciutto, cut into 1-inch pieces; 1 tablespoon extra-virgin olive oil; 1 pound ground beef chuck; 1 pound ground pork; 2 cups dry white wine; 4 tablespoons unsalted butter; 1 large onion, chopped; 1 teaspoon chopped fresh rosemary; 2 bay leaves; Kosher salt; 5 tablespoons tomato paste; 1/2 cup cognac or brandy; 1 28-ounce can whole San Marzano tomatoes; 12 tablespoons unsalted butter; 1/2 cup plus 1 tablespoon all-purpose flour; 1 1/2 teaspoons grated nutmeg; Kosher salt and freshly ground pepper; 6 cups whole milk; 1 1/2 pounds fresh lasagna sheets; 2 tablespoons unsalted butter, softened; 3/4 pound parmesan, grated (2 to 3 cups); 1 pound fresh mozzarella or fontina, grated (4 to 5 cups)