In a large pot, bring chicken broth to a boil.
Add the cut chicken pieces and cook for about 30 minutes or until tender.
Remove chicken, allow it to cool, then shred.
In the same broth, add carrots, celery, and onion; simmer for 10 minutes.
In a bowl, mix flour, baking powder, and salt.
Stir in milk and melted butter until just combined.
Drop spoonfuls of the dumpling mixture into the simmering broth.
Cover the pot and cook for 15 minutes without lifting the lid.
Add shredded chicken back to the pot and stir gently.
Garnish with fresh parsley before serving.