Prepare the sauce In a small saucepan, combine 1/2 cup white wine, the fish stock, vermouth, vinegar, and shallots and bring to a boil over high heat.
Cook until the liquid has almost completely evaporated.
Add the cream and hazelnut oil and boil gently until thickened slightly.
Set the pan aside partially covered.
cook the fish Meanwhile, preheat your oven to 425°F and butter a baking dish just large enough to hold the 4 flounder comfortably without crowding.
Wipe the flounder and season them inside with salt and pepper.
Brush both sides of the fish with clarified butter and place the fish in the baking dish, skin side up.
Press the bread crumbs onto the top of each fish and drizzle the remaining butter over the crumbs.
Pour 1/2 cup of the white wine around the fish, taking care not to moisten the crumbs.
Transfer the pan to the middle of the preheated oven and bake for 13 to 14 minutes.
Have ready 4 heated plates.
Once the fish is cooked and the crumbs are golden brown, remove the dish from oven and carefully transfer the fish to heated plates.
Leave the fish in the turned off oven lightly covered while finishing the sauce.
Stir the shrimp into the thickened sauce and cook just until pink, about 1 to 2 minutes.
Add 2 tablespoons of the tarragon (or 2 teaspoons dried and crumbled), salt, and white and red peppers and taste to adjust the seasonings.
Remove the fish from the oven, blot up any liquid with a paper towel, place 3 shrimp on either side and put some chopped hazelnuts and a sprinkle of tarragon (or parsley) down the middle of each fish.
Spoon the sauce evenly around each of the plates and serve at once.
note: Hazelnut oil should be found next to the olive and vegetable oils if your market carries it.or, perhaps, it will be in the specialty food section.
If it is not there, ask for it.
If enough customers ask for a product, eventually buyers get the idea.
In the meantime, you could substitute walnuts and walnut oil, or 3 tablespoons softened unsalted butter and almonds or pecans.