Place penne pasta, tomatoes, vegetable broth, onion, squash, mushrooms in a large pot. Stir in salt and oregano and then drizzle with olive oil. Cover and bring to a boil, reduce heat to low and cook 10 minutes, stirring every few minutes.
Remove from heat, and stir in basil and spinach. Cover and let stand 10 minutes. Stir before serving. Serve with Parmesan cheese.