Prepare the Chicken Stock: Place chicken, celery, onion, chicken base, salt, and pepper in a large pot, cover with 12 cups of water, and bring to a low boil over medium-high heat. Simmer for about 1 hour until tender.

Remove Ingredients: Carefully remove chicken from the pot and set aside. Discard onion and celery, let chicken cool, then shred the meat.

Make Dumplings: In a large bowl, combine flour and ice water to create dumpling dough, knead lightly, roll out, and slice into strips.

Add Cream Soup: Return broth to medium heat, whisk in cream of chicken soup, stir to combine, and adjust seasoning if needed.

Cook Dumplings: Once broth is boiling, add dumplings one by one, stirring gently, and cook for about 5 minutes until they float.

Finish the Dish: Return shredded chicken to the pot, stir gently, simmer for another minute, and serve hot.