Remove the neck and innards from the chicken and discard.
Place the chicken in a large stockpot with celery, onion, chicken base, salt, and pepper.
Add enough water to cover the chicken, about 12 cups.
Bring to a low boil over medium heat and cook for an hour or until the meat falls off the bone.
Take the chicken out of the stock and set it aside.
Remove the celery and onion using tongs, a strainer, or a fine mesh sieve.
For the dumplings, place the flour in a medium bowl, add cold water, and mix with a fork until the dough becomes shaggy.
Use your hands to bring the dough together, then transfer it onto a floured surface.
Knead a few times to combine, then roll it out to about 1/8-inch thick.
Turn the dough periodically to prevent sticking, adding more flour if needed.
Use a pizza cutter to slice into 1-inch strips, then cut into 2-inch lengths.
Let the dumplings rest.
Once the chicken is cool, remove the meat from the bones, discard the skin, and shred the meat and set it aside.
Return the stock to medium-high heat, add cream of chicken soup, and whisk to combine.
Adjust the seasoning with additional salt and pepper as needed.
If a thicker broth is preferred, whisk 3 tablespoons of cornstarch with 1/4 cup of cool water and stir it into the stock.
Bring to a boil to thicken.
Increase the heat until the broth reaches a rolling boil.
Drop the dumplings in one at a time, ensuring they don’t pile on top of each other, then gently stir.
Let them cook for about 5 minutes until tender and floating.
Add the shredded chicken back to the pot, stir gently, and cook just long enough to warm the meat through.
Serve hot and enjoy.