Bring a generous 2 quarts of water and 1 tablespoon of table salt to boil in a large pot. Using back of the box cooking times as a guide, add pasta to the water, stirring several times at the beginning to prevent sticking. The last 4 to 5 minutes of the pasta cooking time add the winter squash; cook until tender-crisp. The couple of minutes, add the Brussels sprouts and return water to a simmer.

With a large bowl under the strainer to catch the liquid, drain the pasta and return it to the pot. Add pesto and up to 1 cup of the reserved cooking liquid; toss to combine. Serve with grated cheese, if you like, and serve immediately.