Vegetable Moussaka

Name: Vegetable Moussaka
Ingredients: 3 1/2 pounds eggplant, unpeeled, cut into 1/2-inch-thick rounds; 1/2 cup (about) olive oil; 1 large onion, thinly sliced; 1 cup finely chopped peeled carrots; 1 cup finely chopped celery; 4 garlic cloves, minced; 12 ounces portobello mushrooms, cut into 1/2-inch pieces; 1 teaspoon dried oregano; 1/2 teaspoon ground cinnamon; 1 28-ounce can crushed tomatoes with added puree; 1/4 cup chopped fresh Italian parsley; 1 cup grated Parmesan cheese; 6 tablespoons (3/4 stick) butter; 7 tablespoons all purpose flour; 3 1/2 cups whole milk; 4 large egg yolks