For this excellent chicken broth, select a whole chicken that gives you both the neck and giblets, to add flavor to your broth. Ask the butcher to cut up the chicken for you, or cut it up yourself with a poultry shears or sturdy kitchen scissors. If only cut-up chicken is available, buy extra chicken backs to add to the broth to make up for the absence of the neck and giblets. Plan to make the broth at least several hours before you need it, so it can be chilled and the fat, which will solidify on the surface, can be easily lifted off. The broth freezes well. Store it in 1- or 2-cup containers for convenience.

Place the chicken in a large, deep bowl. Add the neck and all the giblets except the liver; reserve the liver for another use. Add ½ cup of coarse salt. Cover the chicken with cold water and refrigerate for 1 hour. Drain and rinse the chicken. Transfer the chicken to a stockpot and add water to barely cover (about 3 quarts).

Add the carrot, celery, onion, cloves garlic, parsley, thyme, and peppercorns to the stockpot. Set the pot over low heat, cover, and heat slowly until just barely simmering. Uncover and watch the pot. As foam rises to the top, skim it off with a fine-mesh skimmer or perforated spoon.

Cook the chicken in the barely simmering water over low heat for about 35 minutes. Use a Chinese mesh strainer or a perforated spoon to lift the legs, thighs, and breasts from the broth and place them on a deep platter, leaving the remaining pieces in the pot. Continue to cook the broth, uncovered, over low heat.

Let the chicken cool for about 20 minutes, or until it can be easily handled. Then pull the skin off the meat, reserving the skin. Pull or cut the cooked chicken from the bones in pieces and reserve separately. Add the bones, any gristle, and the reserved skin to the simmering broth. Continue to cook, uncovered, over low heat for 2 hours longer, or until the broth is reduced to about 2 quarts.

Remove the pot from the heat and let the broth stand for 1 to 2 hours, until lukewarm. Line a fine-mesh strainer with cheesecloth and place over a large bowl. Or, place a chinois over a large bowl. Strain the broth and discard the solids.

If there isn’t room in the refrigerator for the bowl of broth, divide it among smaller bowls or other containers. Cover and refrigerate the broth for several hours or overnight or until is well chilled and the fat has solidified on the surface. Lift off the fat, using the fine-mesh sieve. The broth will keep, tightly covered, in the refrigerator for up to 3 days or in the freezer for up to 4 months.

Use the delicious cooked chicken meat in sandwiches, salads, soups, or as a filling for crepes.