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