My husband and kids get crazy excited when I make this for dinner. It works year-round and when anyone in our house is sick, this is always the most-requested comfort dinner. I do not add any salt to this (except the pinch in the dumplings because of high blood pressure in my household but salt-lovers can always add it at the table if desired.
Put chicken and all seasonings into a pot; cover with water. Boil until chicken is cooked through and falling off the bone. Remove chicken and reserve the water.
Remove all chicken meat from bones and put the meat back into the water. Add the chopped celery and carrot. Taste the broth - adjust seasonings if necessary to suit your tastes. Bring to boil, lower heat, and simmer until carrots are soft.
While soup is simmering, make the dumplings. Combine the baking powder, flour, and salt. Cut the butter into the dry ingredients using a pastry blender or fork. Stir in the milk until the dough forms a ball (add more flour or milk if necessary).
Heavily flour a work surface. Roll the dough out thin (I like to use a heavily floured pasta roller on setting one for this) and cut the dumplings into roughly 1x2 inch rectangles. Make sure the dumplings stay heavily floured throughout to avoid sticking.
Once the carrots are soft and tender, add the dumplings to the soup, stirring while adding to prevent sticking together. Do not shake off the extra flour - it helps thicken the broth. Boil for 15-20 minutes or until the dumplings lose the doughy taste. If you prefer your broth thicker, you can mix 1/8-1/2 cup flour with an equal amount cold water then add this to the stock, boiling at least five minutes to remove the raw flour taste.