Start the soup: Place chicken pieces in a large pot; add chicken stock, onions, celery, and salt. Bring to a boil over medium-low heat, then simmer, partially covered, until chicken is tender, about 15 to 20 minutes.

Meanwhile, make the dumplings: Beat egg and milk together in a large mixing bowl. Mix in 1 cup flour, baking powder, and salt.

Grate cold butter into the wet flour mixture; stir in parsley.

Dollop 6 large spoonfuls of dumpling mixture onto the top of the simmering chicken. Cover the pot and steam dumplings until fluffy, 10 minutes more.

Remove dumplings and chicken pieces to a large dish; shred chicken and discard bones. Cover and set aside, keeping warm.

For the gravy: Strain stock left in the pot, pressing the vegetables to release more flavor; return stock to the pot.

Whisk water with remaining 1/2 cup flour until smooth; stir into the strained stock. Season with pepper and bring to a boil, stirring constantly, to thicken.

Stir in chicken and top with dumplings.

Serve with parsley and enjoy!