Place chicken in your slow cooker. Add onion, celery, carrots, and season with salt and pepper. Pour in bone broth and water. Cover and cook on High for 4 hours, or until carrots are very tender.
Skim any foam or impurities from the surface if needed. Remove chicken and set aside. Strain out the vegetables and transfer them to a blender, along with 1 cup of the broth.
Blend the vegetables until perfectly smooth (be cautious with hot liquids!). Pour the pureed vegetables back into the slow cooker, thinning with more broth if needed.
Add the pastina to the crockpot, cover, and cook on High for 35–45 minutes, or until pasta is tender and soup has thickened slightly.
While pasta cooks, shred the chicken into bite-sized pieces. Stir it back into the crockpot when the pasta is done.
Season the soup with additional salt and pepper to taste. Serve with Parmesan and parsley.
