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In a 12 to 14-inch ovenproof saute pan, heat 4 tablespoons of oil until smoking. Add the mushrooms and garlic and saute 3 minutes. Add the tomato paste and thyme, and continue to cook 5 minutes. Remove the mixture to a bowl and set aside.
Season the fish well with salt and pepper. Heat the remaining oil in the same pan and add the fish. Saute until deep golden brown on the first side. Carefully turn the fish, add the wine, and return the mushroom mixture to the pan. Put the pan into the oven and cook for 4 minutes, until fish is cooked through. Remove from oven, sprinkle with parsley and serve.