Rinse the salmon head and remove the gills, if necessary, leaving the gill plates intact. Using a sharp knife, split the salmon head in halflengthwise. Place the salmon in a 6-quart saucepan and add the onion, garlic, carrot, bay leaf, thyme, and peppercorns to the pan. Add the water and wine. The fish head should be completely submerged; if not, add a bit more water. Bring the liquid to a boil and then reduce to a bare simmer. Partially cover the pot and simmer for 1 hour.

Using tongs or a large, slotted spoon, transfer the pieces of salmon and the vegetables to a large fine-mesh sieve set over a large bowl to catch all the juices. Do not press on the solids. Pour the stock through the sieve into the large bowl. Discard the solids. Let the stock cool. (To cool the stock quickly, set the bowl in a larger one filled with ice water, or a sink with about 2 inches of ice water.) Stir the stock occasionally to help cool it down. Cover and refrigerate the stock for up to 2, days. Once the stock is chilled, skim any congealed fat from the surface using the side of a large spoon. To keep the stock longer, transfer to a freezer container, allowing 1 inch of headspace, and freeze for up to 6 months.