Add the wine, vinegar, shallot, and tarragon to a small saucepan over medium-high heat. Bring to a boil, then reduce the heat to a simmer until the liquid has reduced to about 1½ tablespoons (about 5 to 7 minutes).

Strain the mixture through a fine-mesh sieve, using the back of a spoon to extract as much flavor as possible. Let it cool for 5 minutes.

Melt the butter in a microwave for about 1 minute, until hot. Alternatively, heat it on the stove.

In a high-powered blender, add the egg yolks, infused vinegar, lemon juice, and salt. Blend for 5 seconds until combined.

With the blender running on medium-high, slowly stream the hot butter through the top lid cap opening into the mixture until emulsified.

Pour the sauce into a small bowl, stir in the finely chopped tarragon, and serve while warm.