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For the sauce:
For the sauce, put the Champagne vinegar, white wine, shallots, 1 tablespoon tarragon leaves, 1/4 teaspoon salt, and 1/4 teaspoon pepper in a small saucepan. Bring to a boil and simmer over medium heat for about 5 minutes, until the mixture is reduced to a few tablespoons. Cool slightly.
Place the cooled mixture with the egg yolks and 1 teaspoon salt in the jar of a blender and blend for 30 seconds. With blender on, slowly pour the hot butter through the opening in the lid. Add the remaining 2 tablespoons of tarragon leaves and blend only for a second. If the sauce is too thick, add a tablespoon of white wine to thin. Keep at room temperature until serving.
For the steak:
Season the steaks liberally with salt and coarsely ground black pepper on both sides. Heat a thin layer of olive oil in a large saute pan over high heat until it's almost smoking, then sear the steaks on each side for 1 minute. Lower the heat to low and cook the steaks for about 7 to 10 minutes, turning once, until very rare in the middle. Remove to a plate, cover tightly with aluminum foil and allow to sit for 10 minutes. Serve with the bernaise sauce on the side.
To make the sauce in advance, prepare an hour before serving and allow it to sit in the blender. Before serving, add 1 tablespoon of the hottest tap water and blend for a few seconds.
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