Add the white wine vinegar, 2 tablespoons of water, and the chopped shallot to a small pan. Cook over medium-high heat until the shallots are soft, about 10 minutes and only about 3 teaspoons of liquid remain. Strain this liquid, pressing to extract as much as possible, into the bottom of a jar that barely fits the char of an immersion blender.

To make the sauce, add the yolks, salt, and pepper to the strained vinegar. Melt the butter in a separate glass jar in the microwave until steaming hot (or on the stovetop in a small saucepan). Blend the yolk mixture by running the immersion blender in the bottom of the jar. Without moving the blender head, slowly pour the melted butter in while blending constantly. An emulsion will form. Blend in the tomato paste. Add salt and pepper to taste and stir in tarragon.