In a small saucepan, stir the vinegar, shallot, garlic, tarragon, salt, and pepper together. Bring to a boil and let cook for 2 minutes, until reduced by about half.
Place egg yolks in a medium-size heatproof bowl. Whisk in the vinegar mixture and 1 piece of the butter.
Place the bowl over a pot of barely simmering water. The water should not touch the bottom of the bowl. Cook, stirring rapidly with a whisk until the butter melts and the sauce begins to thicken.
Add the remaining butter, one piece at a time, stirring constantly until melted.
Continue to cook for 2 minutes until the sauce is thick and the temperature reaches 160°F.
Immediately remove the sauce from the heat and serve over beef, pork, chicken, or vegetables.
Make ahead tip
The sauce can be made an hour in advance. Cover and let stand at room temperature.
Video
Notes
White pepper: Black pepper will also work.Makes about 1.5 cups.