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1
Rinse the fish under cold running water until the water runs clear and no trace of blood remains. Cut off the head and tail with a large knife or cleaver. Use a pair of scissors to cut off the fins, including the two lines of fins that run along the sides of the fish. Cut the fish crosswise in half through the backbone and set aside.
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2
Preheat the oven to 450u00b0F.
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3
Peel 1 of the potatoes and slice very thin on a mandoline. As you slice the potato, arrange the slices in a single layer in a spiral fashion, starting in the center of the pan in an ovenproof 8-inch nonstick frying pan, covering the bottom of the pan. Sprinkle with half the thyme, teaspoon of the salt, and pepper to taste and drizzle with 1 tablespoon of the olive oil. Repeat to make a second potato cake in a second pan.
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4
Place one piece of the fish in the center of each potato cake. Put the pans in the oven and roast until the fish is cooked through, about 15 minutes. Transfer the fish to a cutting board.
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5
Return the cakes to the oven to brown, about 5 more minutes. Turn the potato cakes out onto two serving plates.
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6
Combine the tomatoes, wine, and vinegar in another medium frying pan and bring to a boil on top of the stove. Reduce the heat and simmer until the liquid is reduced by one-half and the tomatoes are softened, about 5 minutes. Add the butter, olives, and olive oil and whisk to emulsify. Season to taste with salt and pepper.
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7
Remove the skin and lift the fish fillets from the bones. Place the 2 halves of each fillet on top of each other, in the center of each cake. Arrange 5 tomatoes around each potato cake. Pour the sauce over the fish and scatter the olives around. Garnish each plate with a sprig of rosemary and serve immediately.
