Make the bearnaise reduction first. 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 to cool.
Blend yolks and bearnaise reduction together. With the blender running, add 1/3 of the butter in a slow steady stream. Once it emulsifies, turn the blender speed up to high and add the remaining butter. Season with salt and pepper and set aside in a warm spot to hold the sauce.