In a large skillet, heat the olive oil over medium-high heat. Add the ground beef and Italian sausage and cook for a few minutes until no longer pink.
Transfer the meat mixture to a slow cooker. Add the diced carrots, onion, crushed tomatoes, celery, beef broth, bay leaves, and Italian seasoning. Stir to combine.
Cook on low for 7 to 8 hours or on high for 3 to 4 hours.
Thirty minutes before serving, stir in the drained and rinsed kidney beans, cannellini beans, and uncooked ditalini pasta. Cover and continue to cook until the pasta is tender.
Discard the bay leaves and season with salt and pepper to taste.
Ladle the soup into bowls and sprinkle with shaved Parmesan cheese (if desired). Serve hot with a crusty baguette or breadsticks.
