This recipe was inspired by a recipe I found in a magazine, but I changed it quite a bit to reflect our tastes and memories of what the dish should be. It's a creamy chicken stew with fluffy light dumplings.
Sprinkle the chicken parts with 3/4 tsp salt and 1/2 tsp pepper.
Place the flour in a resealable bag with the flour and 1 tsp poultry seasoning; add about two pieces of chicken at a time and shake the bag to thoroughly coat the chicken, placing the coated chicken on a rack, repeating until all the pieces are coated with flour.
Heat one half of the oil in a large deep chicken fryer skillet, and add the chicken parts; brown for a few minutes on each side until a nicely golden brown color (depending on the size of the skillet, it might take two batches), and set chicken aside.
Add the rest of the oil to the skillet, heat, and add the onion, and carrot; saute until lightly browned and tender.
Add the chicken broth, water, browned chicken, celery, the remaining salt, pepper and poultry seasoning; cover and simmer 30 minutes.
Make the white sauce: Whisk 2 T flour in a saucepan with melted butter for about a minute, then add 1 cup milk, heating until thickened.
Add the white sauce (or can of cream of chicken soup) and frozen peas.
Make the dumplings, mixing all ingredients together and stirring until the dry ingredients are moistened.
Drop heaping tablespoon portions of the dumplings into the simmering chicken/liquid.
Cover and continue to simmer for 12 minutes, or until a toothpick inserted into the dumpling comes out clean.