A sophisticated dish that you are just as likely to encounter in a restaurant as at your next potluck. If you can’t find creme fraiche at your gourmet cheese store or health food store, you can make it yourself (at a fraction of the cost), but you will have to start it a day in advance (see note below).
To make the sauce, combine the shallots and wine in a small saucepan. Bring to a boil and simmer until the wine has almost completely evaporated. Stir in the creme fraiche. Bring the mixture to a boil, stirring constantly. Whisk in the butter, 1 piece at a time, lifting the pan from the heat occasionally to cool the mixture and adding each new piece of butter before the previous one has completely melted. (The sauce should not become hot enough to liquefy.) Add salt and pepper to taste. Keep the sauce warm in the top of a double boiler while you prepare the fish.
To cook the fish, sprinkle the fillets with the thyme, salt, and pepper. Melt the butter in a large heavy skillet. When the foam subsides, add the fish, skin side up, and cook for 2 minutes. Then turn and cook the other side for about 1 minute. Serve with the butter sauce and garnish with parsley.
Note: To make creme fraiche, combine 1 cup whipping cream with 1 teaspoon cultured buttermilk. Heat to 85 degrees F. Cover and let stand at room temperature for 8 to 24 hours, until thickened. Store in the refrigerator.