Ideally, the salmon heads should be split in half. Given that this is difficult, it is best to have it done by the fish supplier. If you just have the whole heads, use them as described here. Remove the gills from the salmon head(s). Rinse with cold water, or, better, soak the head(s) in a bowl of cold water for a couple of hours or overnight (in the refrigerator), changing the water every hour or so.
Melt 1½ounces (45grams) butter in a saucepan and add the carrots, onions, garlic, and salmon head(s). (A)
Add 1cup (250milliliters) of the red wine and stir over medium heat until the vegetables soften and a brown layer of caramelized juices begins to form on the bottom of the pan. This may take as long as 15 minutes. The salmon should completely fall apart (B)
and the liquid should completely evaporate until it forms a caramelized layer on the bottom of the pan. There will also be plenty of fat, which can be spooned off, if practical. (C)
Deglaze the pan with the remaining red wine (D)
and add the bouquet garni. Simmer the sauce gently, stirring occasionally, while scraping with a wooden spoon against the bottom of the pan. (E)
After about 45 minutes, strain the sauce through a fine chinois into a 2-quart saucepan, using a rolling pin to force through the sauce. (F, G)
Place the saucepan on the heat, keeping it to one side of the heat source. Skim off any froth and scum. (H)
Simmer until about 2cups (500milliliters) liquid remain, skimming until the sauce is free of fat.
You can either finish the sauce with butter alone (such a sauce will be more intense and richer, and there will be less of it) or finish it with beurre manié. If you want to finish the sauce with butter alone, reduce the liquid to ¾cup (180milliliters), or until it has the consistency you like, and then whisk in enough butter to get the right effect. You could also omit the butter; keep in mind, however, that the red wine sauce base can take on an acrid quality that is best softened with butter.
If finishing the sauce with beurre manié, work together about 1ounce (30grams) butter with 2tablespoons (15grams) flour. Whisk in 2tablespoons (30grams) of the beurre manié to start, bring to a boil, and judge the consistency. If you want the sauce thicker, add more beurre manié and return to a boil again to assess its thickening power.