Remove the neck and innards from the chicken and discard. Place the chicken in a large stock pot. Add the celery, onion, chicken base, salt, and pepper. Add enough water to just cover the chicken. Place over medium heat and cook at a low boil for about an hour until the meat begins to fall off the bone.

Remove the chicken from the stock and set aside. Pour the stock through a fine mesh sieve to remove the onion and celery.

Make the dumplings by placing the flour in a bowl. Add ice water and stir with a fork until combined. Knead the dough until it forms together, then roll out to about ⅛-inch thick. Cut into 1-inch strips and then into 2-inch lengths. Allow to rest.

Once cool enough to handle, remove the meat from the chicken and shred. Discard the bones and skin. Set the meat aside.

Return the stock to medium-high heat. Add the cream of chicken soup and whisk to combine. Adjust salt and pepper to taste. If a thicker broth is desired, whisk together cornstarch with a bit of water to form a slurry, then add to the broth and bring to a boil.

Bring the broth to a rolling boil. Add dumplings one at a time. Cook for about 5 minutes until tender and floating. Gently add the shredded chicken and stir to combine. Cook until the chicken is heated through.