Preheat oven to 400 degrees F. Season steak on both sides with salt and pepper and refrigerate. Combine wine, vinegar and shallot in a small saucepan and bring to a boil. Reduce heat to medium-low and simmer until mixture is reduced to two tablespoons, 15-20 minutes.
Meanwhile, heat a large, heavy, ovenproof skillet over medium-high heat. When it's hot, add oil and reserved tablespoon of butter. When butter is melted, add steak and sear for one minute. Reduce heat and continue to cook until the first side is golden brown and beginning to crisp, about three minutes longer. Turn the steak with tongs and sear the other side until well-browned, two or three minutes.
Place pan in oven and finish cooking, turning once, 6-8 minutes for medium-rare. Transfer steak to a platter and loosely cover with foil to keep warm. To finish sauce, put it through a fine strainer, pressing on shallots. Whisk the five tablespoons of cold butter a few pieces at a time into warm reduction until you have a creamy sauce. Stir in tarragon to taste and season with salt and pepper. Slice steak into half-inch thick slices across grain, spoon sauce on top and serve.
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