In a small saucepan, combine wine and vinegar, shallots and tarragon stalks. Boil the mass at a low boil, without closing the lid, until the volume is reduced by two-thirds. Take out the tarragon.
In a separate bowl, beat the yolks and 1.5 tsp until foamy. cold water. Put the container in a water bath and continue to beat the eggs for 2-4 minutes until the mixture thickens. Remove the container from the water bath and whisk the mixture to cool slightly.
Introduce it to the wine broth. Add oil, chopped tarragon leaves. Season the mass with salt and ground white pepper to taste. Lightly reduce the sauce.