Combine the wine, half the tarragon, the vinegar, garlic, shallots and some salt and pepper in a saute pan over medium-low heat. Cook until reduced by half. Transfer to a medium metal bowl.
Start to whisk the wine mixture in the bowl while adding the butter in increments. (Do not stop whisking throughout this whole process.) Temper the eggs so they do not scramble and add them to the bowl. The sauce will look glossy and thick. Whisk in the lemon juice, if using. Taste for seasoning.