Combine the wine, vinegar, tarragon, shallot, and pepper in a small sauce pan. Gently simmer until all liquid has evaporated. Set aside to cool.
Melt butter over low heat, or in the microwave until sizzling hot. Pour into a spouted measuring cup.
Place the shallot mixture in the bottom of a narrow glass container.
Add the egg yolks and lemon juice to the mixture.
Place the immersion blender on the bottom of the container and blend to combine the egg yolks with the mixture.
Very slowly pour the melted butter down the side of the container while blending to thoroughly combine. Mixture will start to thicken, and will be bubbly.
Stir in the parsley and add salt if needed.
Store unused sauce in the refrigerator for up to 3 days. Carefully reheat in the microwave before serving.