Remove the chicken neck and gizzards. Place the chicken, onions, carrots, and celery in a large stock pot and cover with water. Bring to a boil, then reduce heat so water maintains a gentle simmer.
Cook chicken for 2-3 hour. I love to cook it for a long time to get a lot of flavor.
Mix flour, baking soda, and salt together in bowl. Cut shortening into flour mixture with your fingertips until it resembles small peas. Add milk a quarter cup at a time, you may not need a full cup.
Stir until a ball of dough just begins to form, being careful not to over mix. On a flour surface roll about 1/4 inch thick.
Using a pizza cutter cut dough into rectangles about 1 inch wide by 2 inches long. Place strips on flour sheet pan and allow to harden for at least 30 minutes or up to several hours.
Once chicken is done, remove from the broth and let cool. Remove chicken from the bone and shred into medium-sized pieces, discarding bones and skin.
Pour the chicken broth through a fine mesh sieve lined with a coffee filter, discarding vegetables. Reserve 6 cups of the broth for the dumplings.
Refrigerate or freeze the rest to use in for another recipe.
In a large pot over medium-low heat, bring broth to a gentle simmer and drop in dumplings.
Cover and allow to cook for 7-10 minutes.
Reduce heat to low and add chicken.
Allow to cook until thickened, about 20 to 30 minutes.
Season generously with salt and pepper.