Place the carcass in a large stockpot. Add the celery, onions, water, salt, peppercorns, and bay leaves.
Bring to a boil, reduce the heat to medium, and simmer, uncovered, for 2 hours. Remove from the heat. Skim any fat that has risen to the surface.
Strain through a large fine-mesh sieve. Reserve any meat that has fallen off the bones and pick off any meat that may still remain on the carcass.
Reserve the onions and celery for gumbo. Use right away or store the broth in quart containers in the freezer.
Yield: 2 quarts