Heat olive oil in a large pot over medium heat. Stir potatoes, carrots, celery, onion, and garlic into pot.
Mix in tomato paste, beans, tomatoes, broth, and water. Season with basil, oregano, and salt. Cook and stir 30-40 minutes, or until vegetables are tender.
Stir pasta into the soup and cook until al dente, about 8 minutes depending on the pasta shape.
Add the chopped spinach the last 5 minutes of cooking. Serve with freshly grated parmesan.