Halve steaks crosswise, then pat dry and sprinkle all over with 1 teaspoon salt and 1/2 teaspoon pepper (total).
Heat a 12-inch heavy ovenproof skillet (not nonstick) over medium heat until hot, then add oil, swirling skillet to coat bottom, and cook steaks 5 minutes per side for medium-rare.
Transfer steaks to a platter and let stand, loosely covered with foil, 5 minutes.
Boil wine, vinegar, shallots, and 1 tablespoon tarragon in a small heavy saucepan until liquid is reduced to 2 tablespoons, then strain through a fine-mesh sieve set into a medium metal bowl, pressing on and then discarding solids.
Whisk yolks into vinegar mixture, then set bowl over a pan of barely simmering water and cook, whisking constantly, until yolks have thickened slightly (do not scramble).
Whisk in butter 1 piece at a time, adding each piece before previous one has melted completely.
Remove from heat and whisk in lemon juice, remaining tablespoon tarragon, 1/2 teaspoon salt, and 1/2 teaspoon pepper (or to taste).
Serve steaks with sauce.
·The egg yolks in the sauce will not be fully cooked.·Béarnaise can be made 20 minutes ahead and kept in bowl, covered, over hot water off heat.
