How to Make It
Preheat oven to 450°F. In a large bowl, toss squash with oil, sage and 1/2 tsp. salt. Spread evenly on a baking sheet; roast until soft, about 15 minutes, stirring once.
Whisk cream, broth and mustard in a large, heatproof bowl. Bring a pot of salted water to a boil. Add fettuccine; cook until almost al dente, 10 minutes or as package label directs. About 2 minutes before pasta is finished, place bowl with cream mixture atop pot to warm it, stirring twice.
Once pasta is done, remove bowl from pot. Drain pasta, reserving 1/2 cup cooking water. Add pasta to cream mixture. Toss in chicken, Parmesan and squash. Add a bit of pasta water if mixture seems dry. Season with salt and pepper.
Sprinkle with parsley, and serve immediately. Pass extra Parmesan at the table.