In a small saucepan, combine the wine, vinegar, shallot, and 1 tablespoon of the tarragon. Boil until the liquid is reduced to 2 tablespoons, 8 to 10 minutes.
Strain the vinegar mixture through a fine-mesh sieve into a medium heatproof bowl. Whisk in the egg yolks.
Set the bowl over (not in) a saucepan of simmering water and cook, whisking constantly, until the mixture has thickened to the consistency of mayonnaise, 3 to 4 minutes.
One piece at a time, whisk in the butter until melted and smooth. Remove from heat and whisk in the lemon juice, the remaining tablespoon of tarragon, and ½ teaspoon each salt and pepper.