Gather Your Ingredients

First, gather and measure (if applicable) all of your ingredients, placing them in a place easy for you to reach by the stove. This makes everything easier.

Make the Vinegar Reduction

In a saucepan, add the white wine vinegar, shallot and fresh tarragon sprigs over medium heat. Let this mixture simmer for around 5 minutes, or until the vinegar has reduced to around 1-2 tablespoons. Strain this vinegar reduction, discarding (or snacking on) the shallots and tarragon sprigs. Return the vinegar to the saucepan and let cool for five minutes.

Emulsify the Eggs and Butter

Turn the saucepan on a medium-low heat and add the egg yolks, water and olive oil, whisking continuously. At first, the mixture will have a watery texture. After only a few minutes, the texture will start to thicken. You don’t want the eggs to scramble, but you want the sauce to turn thick and creamy (like a custard). This happens fast so stay vigilant.

As soon as you see the texture shift, remove the pan from the heat and whisk in the room temperature butter, minced tarragon and salt to taste. Serve immediately.