In a large pot place chicken pieces and add the chicken stock, onion, celery and 2 teaspoons of the salt. Put heat on medium low and simmer, partially covered, 15 to 20 minutes or until chicken is tender.
To Prepare Dumplings: In a large mixing bowl beat together the egg and milk. Add 1 cup flour, remaining salt and baking powder and mix all together. Cut the butter into the flour mixture until the mixture is crumbly. Add 1 tablespoon of the parsley and mix. In 6 large spoonfuls, drop dumpling mixture onto the top of the simmering chicken. Cover the pot and let all simmer for 10 minutes more.
To Make Gravy: Remove chicken and dumplings to a large serving bowl. Cover and set aside, keeping warm. Strain the stock left in the pot, pressing out any 'veggie liquid'. Return stock to pot. Combine water with remaining flour, then stir into the strained stock. Bring all to a boil, stirring constantly, to thicken. Return chicken and dumplings to pot, combing all gently. Serve with remaining parsley.