Boil stock ingredients for 45 minutes to an hour until chicken is 170F internal temperature and remove to cool.
Strain stock and de-fat or refrigerate for use later.
Remove chicken from bone and cut into bite-sized pieces.
For the dumplings, cut the shortening or butter into the flour using a fork or pastry cutter until it's well distributed and in small pieces.
Add milk and mix with a fork until well mixed.
Turn out onto a floured board and knead a few times (skip this step if just making biscuits). Roll out to about 1/8 inch thick on a floured board and cut into stips about 1.5 inches wide and anh length you like. If the dough resists rolling by springing back, wait 5 minutes and roll again.
To make the dish, return the stock to a boil and add chicken and then the dumplings one at a time. Season with salt and pepper to taste and thicken if necessary with a slurry of flour and milk or water to desired thickness. Carrots and celery can be added as well as green peas if desired.