Heat oil in a large nonstick skillet over medium-high heat. Add onion, red pepper, and garlic; sauté 3 minutes. Add squash and parsnip; sauté 10 minutes. Stir in sage, parsley, nutmeg, allspice, 1/4 teaspoon salt, and 1/4 teaspoon black pepper; remove from heat.
Cook pasta according to package directions, omitting salt and fat. Drain in a colander over a bowl, reserving 1 cup cooking liquid. Combine squash mixture, pasta, and 1/4 cup cheese in an 11 x 7-inch baking dish coated with cooking spray, tossing gently to combine.
Melt butter in a medium saucepan over medium heat. Add flour; cook 3 minutes, stirring constantly with a whisk. Add milk; cook 5 minutes, stirring constantly with a whisk. Gradually add reserved cooking liquid; cook 2 minutes or until thick, stirring constantly with a whisk. Add 1/4 teaspoon salt and 1/4 teaspoon pepper.
Pour milk mixture over pasta mixture; sprinkle with 1/4 cup cheese. Bake at 375° for 30 minutes or until lightly browned.