1 roaster chicken or stewing hen, 4-7 lbs
1 onion, unpeeled, cut in half
1 large carrot, ends trimmed, cut in half crosswise
1 large stalk celery, root end removed, cut in half crosswise
12 or so whole black peppercorns
1 bay leaf
Place chicken in a large stockpot with remaining ingredients. Add cold water to cover. Place over high heat until water comes to a boil; then reduce heat to simmer, skim any scum that rises to the top, and simmer, partially covered, for 2 hours. Remove the chicken bits from the pot (it should fall apart, so dig around and make sure you get all the bones out), and remove the veggies, too; then raise the heat to medium. Let the stock boil down until it is reduced by half. Cool for 30 minutes, then strain through cheesecloth or a fine-mesh strainer into a clean stockpot.
(Note: the incredibly overcooked chicken will have almost no flavor, but you can salvage the larger pieces of breast and thigh meat. Chop them, mix with celery and mayonnaise and a bit of mustard, add black pepper, and you'll have a decent chicken salad. Discard the rest.)
To turn your stock into cold-banishing chicken soup, add fresh chopped carrots, celery, and parsley to the pot (add as much as looks good to you for the amount of stock you have). Bring to a boil, then reduce to simmer. Add your favorite egg noodles or small pasta like ditalini, and cook until the noodles are done. Eat while it's hot; it will make your nose run, but you'll feel better.