Combine squash, 1 tablespoon oil, sage, garlic, 1/2 teaspoon salt, and black pepper in a large bowl; toss to coat. Arrange squash mixture on a baking sheet coated with cooking spray. Bake at 425° for 30 minutes or until squash is tender. Cool slightly; peel garlic. Place squash and garlic in a bowl; partially mash with a fork.
Heat remaining 1 tablespoon oil in a large Dutch oven over medium-high heat. Add onion, and sauté for 4 minutes. Reduce heat to medium-low; continue cooking for 20 minutes or until golden brown, stirring frequently. Place onion in a bowl.
Add 2 tablespoons water and spinach to Dutch oven; increase heat to high. Cover and cook 2 minutes or until spinach wilts. Drain in a colander; cool. Squeeze excess liquid from spinach. Add spinach to onions.
Heat 4 1/2 cups milk, bay leaf, and thyme in a medium saucepan over medium-high heat. Bring to a boil; remove from heat. Let stand for 10 minutes. Discard bay leaf and thyme. Return pan to medium heat. Combine remaining 1/2 cup milk and flour in a small bowl. Add to pan, stirring with a whisk until blended. Bring to a boil; reduce heat, and simmer for 5 minutes or until thickened, stirring constantly. Remove from heat; stir in remaining 1/2 teaspoon salt, 1 1/4 cups cheese, red pepper, and nutmeg.
Spread 1/2 cup milk mixture in bottom of a 13 x 9-inch glass or ceramic baking dish coated with cooking spray. Arrange 3 noodles over milk mixture; top with half of squash mixture, half of spinach mixture, and 3/4 cup milk mixture. Repeat layers, ending with noodles. Spread remaining milk mixture over noodles. Bake at 425° for 30 minutes, and remove from oven. Sprinkle with remaining 1/4 cup cheese.
Broil 2 minutes or until cheese is melted and lightly browned. Let stand 10 minutes before serving.