For the ragu:
1 ounce dried porcini mushrooms
2 tablespoons extra-virgin olive oil
1 medium onion, chopped
1 large carrot, finely chopped
1 stalk celery, finely chopped
4 cloves garlic, chopped
2 tablespoons tomato paste
2 portobello mushroom caps, chopped
1 1/2 pounds shiitake mushrooms, stems removed, chopped
Kosher salt and freshly ground pepper
2 28 -ounce cans whole San Marzano tomatoes, crushed by hand
3 bay leaves
1/4 cup chopped fresh parsley

For the lasagna:
3 ounces parmesan cheese, grated
1 1/2 pounds part-skim mozzarella cheese, shredded
8 ounces asiago cheese, shredded
2 pounds ricotta cheese
2 large eggs, lightly beaten
1 pound frozen chopped spinach, thawed and squeezed dry
1/4 teaspoon freshly grated nutmeg
12 ounces dried lasagna noodles