In a small saucepan, combine the tarragon, shallots, vinegar and wine over medium-high heat. Bring to a simmer and cook until reduced by half. Remove from heat and set aside.
Place a stainless steel bowl in a saucepan containing simmering water, or use a double boiler. Whisk the egg yolks until doubled in volume. Slowly add the melted butter, continue beating until sauce is thickened. Stir in reserved shallot reduction. Season with salt and pepper, set aside wrapped in a warm spot.