Remove the neck and innards from the chicken and discard. Place the chicken in a large stock pot. Add celery, onion, chicken base, salt, and pepper. Add enough water to just cover the chicken - about 12 cups. Cook at a low boil for an hour or until the meat begins to fall off the bone.

Remove the chicken from the stock and set aside. Remove the onion and celery from the pot.

Make the dumplings by mixing flour and cold water in a bowl. Form dough and roll it out to about ⅛-inch thick. Cut into 1-inch strips and then into 2-inch lengths.

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

Return stock to medium-high heat. Add cream of chicken soup and whisk to combine. Adjust seasoning as needed. For thicker broth, mix cornstarch with cool water to form a slurry and add to the broth.

Bring the broth to a rolling boil. Add dumplings one at a time. Cook for about 5 minutes or until tender. Add shredded chicken and stir to combine, cooking until heated through.