Mushroom Lasagna

INGREDIENTS

• 2 pounds portobello mushroom caps, gills removed, caps halved and sliced crosswise ¼-inch thick
• ¼ cup olive oil, divided
• Salt and pepper
• 1 cup water
• ½ ounce dried porcini mushrooms, rinsed
• 2 pounds red onions, chopped fine
• 8 ounces white mushrooms, finely minced
• 4 garlic cloves, minced, divided
• ½ cup dry vermouth
• 3 tablespoons unsalted butter
• 3 tablespoons all-purpose flour
• 3½ cups whole milk
• ¼ teaspoon ground nutmeg
• ¼ cup plus 2 tablespoons minced fresh basil, divided
• ¼ cup minced fresh parsley, divided
• 12 no-boil lasagna noodles
• 8 ounces fontina cheese, shredded (2 cups)
• 1½ ounces Parmesan cheese, grated (¾ cup)