Bring all ingredients except parsley & marjoram to a boil in a 12-quart stockpot over medium-high heat, then immediately turn down to a bare simmer. Continue to simmer, uncovered, for at least two to three hours and up to six or longer; for the right simmer, look for a few bubbles to slowly rise to the surface every now and then.
If you have used the vegetable trimmings (see note) instead of or in addition to whole veggies, there will be no need to skim the broth. If not, skim any foam as it rises to the surface.
If there is a lot of meat left on the carcass, pull bones out as soon as the meat has softened enough to easily remove from the bones, usually about 45 minutes to an hour into the cooking process. Remove the meat and refrigerate it. Replace the bones and continue to simmer.
Add parsley and marjoram about at about two hours before you plan to stop cooking then continue to simmer till stock is rich and flavorful, about 2 hours longer. When finished, strain stock. Cool stock about 20 minutes, skim fat from surface or divide up into containers and cool, then skim fat after it has hardened on the surface.
Use as a base for soup or portion and freeze.
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