Heat olive oil in a large stock pot. Add the onion carrots and celery and sauté until the vegetables are soft, about 5 minutes.
Add the chicken broth and bring to a simmer.
Add the pasta and cook until it is tender, about 6 minutes.
Add the meatballs, and cook for 2 minutes more. Taste the soup and season with salt and pepper.
Add the spinach and cook just until the spinach wilts, about a minute more.
Ladle into bowls and serve with a sprinkle of parmesan cheese.