Add the vegetable broth, diced tomatoes, kidney beans, cannellini beans, carrots, celery, onion, and Italian seasoning to the slow cooker. Stir once to combine.
Cover and cook on low for 6 hours.
Stir in the dry pasta, cover again, and cook for 30 more minutes until the pasta is tender.
Taste and add salt and black pepper as needed.
Ladle into bowls and top each serving with grated Parmesan cheese.