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 - about 12 cups. Cook the chicken 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 with tongs, a strainer, or by pouring the stock through a fine mesh sieve.

Make the dumplings by placing the flour in a medium bowl. Add the cold water and stir with a fork until combined. Use your hands to work the dough until it forms together. Turn the dough out onto a floured surface and knead a few times to ensure everything is combined. Roll the dough until it's about ⅛-inch thick.

Cut the dough into 1-inch strips then cut each strip into about 2-inch lengths. Allow the dumplings 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. Add additional salt and pepper gradually to taste. For a thicker broth, whisk 3 tablespoons of cornstarch with ¼ cup of cool water to form a slurry and whisk it into the broth.

Bring the broth to a rolling boil. Add the dumplings to the stock one at a time, stirring gently. Cook for about 5 minutes or until they are tender and begin to float. Gently add the chicken to the pot and stir to combine.