Remove legs, thighs, wings, and any stuffing from carcass. Remove any meat still on bones (chop and refrigerate for use in soup). Place carcass, bones, and remaining ingredients in a stockpot (you may have to crack the bones to fit your pot). Add just enough cold water to cover bones by 1 inch. Bring mixture to a boil, reduce heat, and simmer for 4 hours, skimming frequently and discarding any white foam that forms on the surface. Remove from heat and cool.
Strain stock through a cheesecloth-lined colander or a fine sieve into a large bowl; discard bones, vegetables, and seasonings. Cool, then cover and refrigerate overnight. Once stock has cooled sufficiently for fat to solidify, remove and discard fat from top before using.