Create the vinegar reduction: Heat a small frying pan over medium-low on the stove. Once hot, add vinegar, shallot, black pepper, and chopped tarragon. Let the mixture simmer for 10-15 minutes, until well-reduced with no more than a few Tablespoons of liquid left. Then, set aside.
½ cup White wine vinegar, 1 Shallot minced, 1½ Tablespoons Tarragon, 1 teaspoon Black pepper
Prepare the double boiler: In a small saucepan, heat 1-inch of water. While the water heats, combine the cooled vinegar reduction with egg yolks and a splash of water in a metal mixing bowl. Place this mixing bowl on top of the water-filled saucepan, making sure the water does not touch the bowl (alternatively, use a double boiler).
2 Egg yolks
Add butter and stir, stir, stir: While whisking continuously, melt butter into the mixture by adding 2 to 4 Tablespoons at a time. Whisk until each addition fully melts before adding more butter.
1½ sticks Unsalted butter
Once the sauce reaches your desired thickness, remove it from the heat and serve. Enjoy!
Notes
Make sure to maintain a low cooking temperature while making the sauce to avoid scrambling the eggs. This is why using a double boiler (or making one yourself using a metal bowl and pot) is important. The heat should never directly touch the sauce mixture.
Make sure to let the herb vinegar reduction cool before adding it to the other ingredients, or you will scramble the eggs.
If the sauce thickens too much, add a small splash of water while whisking.
Make sure to consistently whisk while making this sauce when adding the butter. You don't want to step away or stop while it cooks.