Cook pasta according to package directions, omitting salt and fat. Keep warm.
Heat oil in a Dutch oven over medium-high heat. Add mushrooms, onion, and garlic; cover and cook 3 minutes. Uncover; cook 5 minutes or until tender, stirring occasionally.
Combine chopped sage and milk in a medium saucepan over medium heat. Bring to a simmer. Combine cornstarch and water, stirring with a whisk. Add cornstarch mixture and cheese to milk mixture, stirring with a whisk. Cook 2 minutes or until thick and smooth, stirring constantly. Remove from heat; stir in pumpkin, salt, pepper, and nutmeg.
Add pasta and pumpkin mixture to mushroom mixture; toss well to combine. Garnish with fresh sage sprigs, if desired.