Divide the squash, onions, and garlic on two baking sheets. Drizzle with olive oil and season with 2 teaspoons of salt and 1 teaspoon black pepper, toss to coat. Roast for 25 - 30 minutes or until the vegetables are tender and starting to brown, flipping the vegetables once with a metal spatula.
While the vegetables are roasting, bring a large pot of salted water to a boil. Cook the pasta according to the package directions. Reserve one cup of the pasta cooking water, drain the pasta and rinse with hot water. Return the pasta to the hot pot. Add the roasted vegetables to the pot along with the reserved pasta water, the parsley, Parmesan cheese, and walnuts. Toss well to coat. Season to taste with more salt and pepper if desired.
Serve the pasta with a drizzle of olive oil and more Parmesan cheese if desired.