Ingredients

• 2 (1 1/4-inch-thick) boneless rib-eye steaks (16 ounces each)
• 1 tablespoon vegetable oil
• 1/4 cup dry white wine
• 1/4 cup white-wine vinegar
• 1/4 cup finely chopped shallots
• 2 tablespoons chopped fresh tarragon, divided
• 3 large egg yolks
• 1 stick unsalted butter, cut into 8 pieces
• 1/2 teaspoon fresh lemon juice, or to taste
• Accompaniment: shoe string potatoes

Instructions

1. Halve steaks crosswise, then pat dry and sprinkle all over with 1 teaspoon salt and 1/2 teaspoon pepper (total).
2. 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.
3. Transfer steaks to a platter and let stand, loosely covered with foil, 5 minutes.
4. Make béarnaise while steaks stand: 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.
5. 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.
6. 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).
7. 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.