In a mixing bowl, combine the ground turkey, breadcrumbs, egg, Italian seasoning, salt, and black pepper. Mix gently until just combined, then roll the mixture into 1-inch meatballs and set them aside.
Add the diced carrots, celery, onion, and minced garlic to the slow cooker. Pour in the diced tomatoes with their juices, the drained cannellini beans, and the chicken broth. Stir to combine.
Gently place the turkey meatballs on top of the vegetables and broth. Cover and cook on low for 6 hours or on high for 3 hours.
About 30 minutes before serving, stir in the small pasta. Cover again and cook until the pasta is tender. Stir in the fresh spinach until it wilts.
Ladle the soup into bowls and top each serving with grated Parmesan cheese.