Place chicken in the bottom of a large slow cooker (at least 6-quarts). Place onion, celery, and garlic on top of the chicken.
Add Italian seasoning, ½ teaspoon salt, and ¼ teaspoon pepper.
Pour in chicken broth, cover the slow cooker with the lid, and cook on LOW for 6-8 hour or HIGH for 3-4 hours, or until the chicken is tender.
Shred the chicken into bite-size pieces using two forks.
In a medium bowl whisk together cornstarch and half-and-half. Pour this mixture into the slow cooker.
Add gnocchi and shredded carrots to the slow cooker and cover the slow cooker. Increase the heat to HIGH (if you previously had it on LOW). Cook for 45-60 minutes, or until the soup is thickened and the gnocchi is cooked through.
Stir in chopped spinach, cover, and cook for 3 more minutes or until the spinach wilts.
Season with salt and pepper and serve with freshly grated Parmesan cheese.