During the last 5 minutes of the pasta cooking, heat the oil in a large nonstick skillet over medium heat. Add the spiralized zucchini and cook, tossing gently until just tender, about 2 minutes. Season with 1/4 teaspoon each salt and pepper then fold in the spinach, cooked pasta and sauce and some reserved cooking liquid if mixture seems dry. Serve with additional Parmesan, if desired.