In a large soup pot, combine the chopped cooked chicken or turkey, chopped celery, cream of chicken soup, chicken broth, and measured water. Stir well, and bring to a boil over medium-high heat.

Once boiling, cover the pot and let it simmer gently on low heat while you prepare the dumplings.

In a mixing bowl, blend self-rising flour and shortening until crumbly. Gradually stir in the boiling water until a soft dough forms.

Lightly flour a surface, roll out the dough to about 1/8 inch thickness, and cut it into small squares or desired shapes for your dumplings.

Remove the pot lid and drop the dumpling squares into the simmering broth in batches, covering the pot after each addition.

Once all dumplings are added, reduce the heat to low and simmer uncovered for 20 minutes, stirring occasionally.

Taste the broth and adjust the seasoning with salt and pepper as needed. Serve hot.