Remove any bones from fish. Season fillets lightly with salt and freshly ground white pepper.
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Melt 2 tablespoons butter in each of 2 large non-stick skillets big enough to accommodate fish in one layer.
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Place fish flesh side down in melted butter. Cook over medium heat until opaque and lightly golden. Turn fish over with spatula and increase heat a bit. Cook skin side down until skin begins to crisp. When fish is cooked, transfer to platter.
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Combine pan juices in 1 pan. Quickly add champagne, turn heat to high, and reduce to 1/3 cup. Reduce heat to very low. Cut remaining 4 tablespoons butter into small bits and add to pan, whisking until sauce is thick and creamy. Add a pinch of salt and freshly ground white pepper. Drizzle over fish. Serve immediately. |