Preheat the oven to 350 degrees F. or preheat the broiler.
Pound the fish slices until they are evenly 1/8-inch thick.
Put 4 heat resistant plates in the oven or under the broiler until hot. Remove and brush each 1 with 1/2 teaspoon of the butter.
Season the paillards of fish with salt and pepper and put 1 on each plate. Mix the fish stock, ginger, garlic, and tomatoes in a saute pan. Bring to a boil and cook 2 minutes. Whisk the remaining butter into the sauce and pour it over the fish.
By the time you garnish the plates with the cilantro, the fish will be done.
Wash the fish carcasses, removing the gills from the heads, and, under running water, scrape away any blood from the backbone.
Put the celery, onion, herbs, and salt in a pot. Add 1 cup of the water, cover, and sweat the mixture over low heat for 10 minutes. Do not let any browning occur.
Add the fish carcasses and remaining water. Bring to a boil over high heat. The moment it boils, lower the heat to a bare simmer. Stir the bones around very gently for a few seconds so that any coagulated albumin trapped at the bottom will rise to the surface. Skim off any scum, avoiding floating vegetables or herbs. Simmer uncovered for 20 minutes.
Add the wine, and simmer for another 10 minutes. Remove from the heat, let sit for 5 minutes, then carefully ladle all the stock into a fine strainer set over a container. Do not press down on any fish in the strainer. Put the last of the stock into the strainer and discard the debris. Immediately refrigerate the stock uncovered. When cold, cover and keep refrigerated or frozen until needed.
The best fish to include in a light stock to be used for cream and butter sauces are sole, turbot, halibut, and trout. For fish soups and hearty stews, use whatever non-oily fish bones and heads you have: the fished already mentioned plus bass, grouper, snapper, haddock, etc. Despite what most cookbooks tell you, fish stocks should be brought to a boil as fast as possible so that the albumin coagulates and rises to the surface for skimming. Simmer for no more than 30 minutes or the stock will tasty "fishy" and stale. The vegetables have to be finely chopped so that they cook entirely in this short time, and the acid from the wine is necessary if you are to use the stock for making butter sauces, but add it only after the vegetables have given up most of their flavor (it impedes this process if added at the beginning). Any leftover stock can be frozen for up to a month.
Recipe courtesy of Jeremiah Tower, Jeremiah Tower Cooks, Stewart Tabori and Chang, 2002