Preheat the oven to 400F;. Lightly grease 2 large rimmed baking sheets with some of the softened butter. Evenly divide the parsley and tarragon sprigs into 2 bundles and stuff 1 bundle into the cavity of each fish. Set the turbot on the baking sheets, dark-skinned side up and season generously with sea salt and pepper. Dot them with the remaining softened butter.
Pour half of the wine onto each baking sheet and loosely cover the fish with lightly greased foil. Bake on the middle and bottom racks of the oven for 50 minutes, or until a knife inserted into the thickest part comes out easily. Halfway through cooking, shift the baking sheets from top to bottom and from front to back and baste the fish with the pan juices. Remove the fish from the oven and let stand, covered, until serving time.
Meanwhile, make the sauce. In a small saucepan, melt the 2 sticks of butter. Skim the foam from the surface and let the butter cool slightly.
In a medium stainless steel bowl, whisk the egg yolks with the water until frothy. Set the bowl over but not in a pan of barely simmering water and whisk the yolks constantly until slightly thickened, about 4 minutes. Remove the bowl from the pan of water and whisk in the melted butter in a very thin stream; leave any milky solids behind. Continue whisking until the sauce is quite thick. Whisk in the lemon juice and the chopped parsley and tarragon; season the sauce with sea salt and pepper. Keep the hollandaise sauce warm in a pan of warm water.
Remove the dark skin from 1 of the fish. Run a thin metal spatula along the central bone to separate the fillets. With the spatula, lift up the fillets and transfer them to a large warmed platter. Carefully lift up the bones and discard. Scrape the 2 remaining fillets clean and, using the spatula, lift them off the bottom skin and transfer them to the platter. Repeat with the second fish so that you have 8 fillets. Transfer the fillets to plates, spoon some of the sauce on top and serve. Pass the remaining hollandaise sauce at the table.
