Bianca Lasagna with Pesto

Name: Bianca Lasagna with Pesto
Ingredients: 8 ounces fresh asiago, shredded (2 cups); 6 ounces mozzarella, shredded (1 1/2 cups); 3 ounces Parmesan, grated (1 cup); 1 1/2 cups ricotta; 1 large egg, beaten; 3 tablespoons unsalted butter; 1 medium shallot, minced; 1 clove garlic, minced; 3 tablespoons all-purpose flour; 2 1/2 cups whole milk; 1 1/2 cups low-sodium chicken broth; 1/4 cup plus 2 tablespoons prepared pesto; Kosher salt and cracked black pepper; 4 large fresh pasta sheets (8- by 10-inch sheets); 2 tablespoons olive oil; Nonstick cooking spray, for coating aluminum foil; 1/4 cup pine nuts, roasted; Chiffonade of fresh basil, for topping