In a dutch oven, combine the chicken pieces, celery, carrots, onion, broth, parsley, bouillon, salt and pepper, and add enough water to cover.
Bring to a boil, then reduce to low heat, and cover to simmer for about 2 hours, or until the chicken is cooked through.
Remove the chicken pieces; allow them to cool. Then, remove any skin and bones, and shred the chicken up. Return the chicken to the pot.
Add more salt and pepper, to taste.
Return the soup to a simmer.
In a mixing bowl, combine the dumpling ingredients, and mix well to form a stiff dough. (It’ll be very thick and stiff.)
Drop by tablespoonfuls into simmering soup. Cover and allow to simmer for about 20 minutes more. Best if served immediately.