Preheat oven to 450°.
Combine squash, potato, 1 cup chopped onion, and oil in a roasting pan coated with cooking spray, tossing to coat vegetables. Bake at 450° for 30 minutes or until vegetables are tender, stirring once; set aside.
Combine remaining 1 cup onion, milk, nutmeg, cinnamon, and bay leaf in a medium saucepan over medium-high heat; bring to a simmer. Remove from heat; let stand 15 minutes. Strain milk mixture through a fine sieve over a bowl; discard solids. Wipe out the inside of the pan well with paper towels. Return milk mixture to pan. Weigh or lightly spoon flour into a dry measuring cup; level with a knife. Add flour, salt, and pepper to milk mixture, stirring well with a whisk. Cook over medium heat 10 minutes or until thick, stirring frequently. Remove from heat; stir in Parmigiano-Reggiano cheese.
Preheat oven to 375°.
Spread ½ cup milk mixture in bottom of a 13 x 9–inch baking dish coated with cooking spray. Arrange 3 noodles over milk mixture; top with half of squash mixture, ½ cup mozzarella, and 1 cup milk mixture. Repeat layer with noodles, squash mixture, mozzarella, and milk mixture. Top with remaining 3 noodles. Spread remaining milk mixture over noodles, and sprinkle with remaining ½ cup mozzarella. Cover with foil coated with cooking spray.
Bake at 375° for 30 minutes. Uncover and bake an additional 20 minutes. Let stand 10 minutes before serving.