3 or 4 whole carcasses, including heads, of non-oily fish such as sole, turbot, rockfish or snapper
2 tablespoons butter
2 onions, coarsely chopped
1 carrot, coarsely chopped
several sprigs fresh thyme
several sprigs parsley
1 bay leaf
1/2 cup dry white wine or vermouth
1/4 cup vinegar
about 3 quarts cold filtered water
Ideally, fish stock is made from the bones of sole or turbot. In Europe, you can buy these fish on the bone. The fish monger skins and filets the fish for you, giving you the filets for your evening meal and the bones for making the stock and final sauce. Unfortunately, in America sole arrives at the fish market preboned. But snapper, rock fish and other non-oily fish work equally well; and a good fish merchant will save the carcasses for you if you ask him. As he normally throws these carcasses away, he shouldn’t charge you for them. Be sure to take the heads as well as the body—these are especially rich in iodine and fat-soluble vitamins. Classic cooking texts advise against using oily fish such as salmon for making broth, probably because highly unsaturated fish oils become rancid during the long cooking process.
Melt butter in a large stainless steel pot. Add the vegetables and cook very gently, about 1/2 hour, until they are soft. Add wine and bring to a boil. Add the fish carcasses and cover with cold, filtered water. Add vinegar. Bring to a boil and skim off the scum and impurities as they rise to the top. Tie herbs together and add to the pot. Reduce heat, cover and simmer for at least 4 hours or as long as 24 hours. Remove carcasses with tongs or a slotted spoon and strain the liquid into pint-sized storage containers for refrigerator or freezer. Chill well in the refrigerator and remove any congealed fat before transferring to the freezer for long-term storage.
*** Source: http://westonaprice.org/