Step 1Remove the chicken giblets, if there are any. Peel and quarter the onion. Quarter the carrots and celery stalks.
Step 2If you have a heavy-bottomed stock pot with a lid that can accommodate two chickens, use it. If not, a cheap aluminum pot and a heat-diffusing pad over the burner will be fine. The idea is to avoid hot spots on the bottom of the pot. Providing good heat distribution ensures that the stock and chicken don't cook too hard, too fast.
Step 3 Place the chickens, carrots, celery, parsley, thyme, bay leaf, salt and peppercorns in the pot. Place the chickens breast down, so the white meat will be least likely to overcook. Now add the wine, which will not be enough to cover the chicken. So add water until the birds are almost submerged.
Step 4Cover the pot and bring to boil over medium heat, then reduce heat so that the cooking liquor simmers, not boils. Adjust the lid to allow steam to escape. Simmer for 40 minutes, or until the chicken is tender. Turn off the heat.
Step 5Using large slotted spoons, remove the chickens to a large plate and allow to cool. Remove the skins and, as neatly as you can, remove the legs and the meat. Discard the fat. Discard the bones.
Step 6Strain the cooking liquor and discard the vegetables. Return the liquid to the pan and heat, bringing to a boil, then reducing to simmer. Continue to cook, skimming fat as it rises, until the stock is reduced by roughly half. Strain the stock through muslin, allow it to cool to room temperature, and either store it in the refrigerator or freeze it. This will be a superb chicken stock.
Step 7Serve the flavorful dark meat with a green salad and some potatoes finished in a frying pan with chicken stock, butter, sea salt and pepper. Use the white meat in sandwiches or chicken salad. Both will be tender and intensely flavorful and can be served as elaborately or as simply as one wishes.