Cut up the chicken if you want, but you don't have to. On the other hand, if you bought a tray of chicken parts, go for it. Rinse and put in a stockpot and add at least 2 quarts water, enough to cover the chicken. Add the celery, onion, bullion and/or house seasoning, and bay leaves. Bring to boil, lower to a medium bowl, cover mostly, and cook for 45 minutes to an hour, until chicken is done. Remove the chicken from the pot and put it on a plate to cool a bit. Stir in the cream of whatever soup or your own white sauce to thicken up the broth a bit. Turn down the heat and leave it simmering.
When you can handle the chicken, pull off the meat and cut or tear into large chunks. Remove the bay leaves at this point too. Discard the skin and bones. (I actually had started some broth from the neck and gizzard when I started the rest so I just added the bones to that pot and simmered through dinner to make a decent couple of cups of broth to freeze. That's why the site is called CheapCooking! )
Mix the cream of whatever soup in and add the chicken chunks. Let the soup continue to simmer.
In a mixing bowl, mix together the flour, salt, baking powder, parsley, and a pinch of cayenne pepper. Add the milk and blend. Drop the dough by small spoonfuls into the simmering broth. Do NOT stir at this point, they say, or the dumplings will break apart. Just tilt the pot and move it in a circular motion to get the broth around all the dumplings so they cook as separate pieces. Cover and simmer 15 minutes or so. I suspect the timing is not crucial.