Wash and chop carrots, celery, onion, and zucchini; set aside with zucchini separated.
In a slow cooker, combine broth, tomatoes, beans (rinsed and drained of liquid), carrots, celery, onion, thyme, sage, bay leaves, salt, and black pepper. Cover and cook on low for 6 to 8 hours or on high for 3 to 4 hours.
Thirty minutes before the soup is done cooking, add pasta, zucchini, and spinach. Cover and cook 30 more minutes. Season to taste, adding more salt and black pepper if desired. Ladle soup into bowls and sprinkle grated Parmesan cheese over top.