The amount of roux needed to thicken this gumbo will vary with the type of chicken used, since some of the liquid will evaporate during the long cooking needed with a stewing hen or a large roaster. If using small frier pieces that cook quickly, use 1 1/4 cup roux; if using a larger or tougher chicken, use just 1 cup. For the richest flavor, start the stock cooking first, and let it simmer while you measure and cut up the other ingredients. Bring chicken broth and the water to a boil in a large stockpot. Add the neck and back (and wingtips, heart, gizzard and feet, if desired), the parsley stalks and the yellow onion. Return to a boil; skim, reduce heat, and simmer while preparing other ingredients. Mix together the salt, cayenne and black pepper, and season the remaining chicken pieces on both sides with the mixture (reserving any extra seasoning). Film a large skillet with oil and, over high heat, lightly saute the chicken pieces on both sides just until they begin to color. (Or, you can broil chicken briefly, about 5 minutes per side, turning once.) Do not totally brown the chicken; cook it only long enough to tighten the meat and seal in the juices. Reserve chicken pieces. (Add any juice from the bottom of the broiling pan to the stock.) Return stock to a boil, remove from heat and, stirring strongly, blend in a large spoonful of the room-temperature roux. Return pot to low heat so the liquid bubbles gently but does not boil, and gradually stir in the remaining roux, a little at a time, until the liquid thickens slightly. This process will take 5 to 10 minutes. Add sausages and parley to the stock and simmer, uncovered, for 20 to 30 minutes.
Drop the chicken pieces carefully into the stock, add any reserved seasonings, and simmer uncovered, stirring occasionally, for 20 to 30 minutes. Adjust heat to maintain a steady simmer; DO NOT BOIL. Add green onions and celery and continue to simmer until chicken is cooked through but not yet falling off the bone (about 15 minutes longer for a fryer, 1 hour longer if using a tough stewing hen). As chicken simmers, tilt the pot and, using a large metal spoon, skim excess fat from the surface of the broth. Taste carefully and correct seasonings if needed. Remove any chicken parts you don't want to serve (such as feet, neck, upper back). [Do NOT remove if you're gonna serve it to ME... S.C.] If liquid has gotten too thick (it should not be as thick as a stew), stir in a little more broth or water and simmer briefly to blend flavors. Serve gumbo hot over a mound of rice. NOTE: if there is no time to simmer the neck and back, replace water with a light (uncondensed) chicken broth. Serves 5 or 6. GUMBO FILE: Sprinkle about 1/4 teaspoon file power into each person's empty gumbo bowl, then spoon in the gumbo and rice and stir together. CHICKEN OKRA GUMBO: Wash 1 pound okra, trim off the heads and tough tails, and cut into 1/4-inch slices. Make gumbo as above, but decrease roux to 2/3 cup.
Once the roux has been stirred into the liquid, add all the okra at once. (Gumbo liquid will suddenly become much thicker.) Proceed as above, cooking the gumbo for at least 45 minutes after adding the okra, or until okra is very tender. Although gumbos combining both okra and file powder are rare, file powder may be sprinkled into the gumbo bowls if desired.