Make a reduction: Boil the the white wine vinegar, lemon juice, half the tarragon and the shallots until reduced by half. Strain and allow to cool
Mix together the egg yolks and reduction then whisk in a glass bowl over a bain-marie until the mixture is thick and able to coat the back of a spoon
Remove from the heat and slowly start to drizzle in the butter whisking all the time until all the butter is incorporated
Add the remaining tarragon and season with salt and pepper
*TIPBe careful not to overheat when whisking as this will cause the sauce to split. If the sauce appears to be on the verge of splitting, as indicated by a slight greasy appearance, take it off the heat and whisk in a dash of cold water.