Add the diced tomatoes, tomato paste, sun-dried tomatoes, vegetable broth, carrots, celery, onion, garlic, oregano, rosemary, bay leaves, salt, and pepper to the slow cooker.
Cook on LOW for 7 hours or HIGH for 4 hours.
Add the kidney beans, great northern beans, zucchini, ditalini pasta, frozen green beans, and spinach. Cook for an additional 30–45 minutes, or until the pasta and vegetables are tender.
Remove the bay leaves and serve with Parmesan cheese.