Step 1

Clarify the butter by melting it in a small, heavy-based saucepan over a low heat. When the butter is foaming, remove the pan from the heat and leave it to stand for a few minutes so that the white solids sink to the bottom of the pan. Sieve the butter through a fine sieve and discard the solids.

Step 2

Pour the vinegar into a non-reactive saucepan. Add the shallots, chopped tarragon and salt, to taste. Heat gently over a medium heat until the volume of liquid has reduced by more than half. Strain and set aside until completely cooled.

Step 3

Lightly beat egg yolks with one teaspoon of water. Stir the egg yolk mixture into the cooled vinegar, then add the lemon juice.

Step 4

Pour the mixture into a bowl suspended over a pan of simmering water (do not allow base of the bowl to touch the water). Whisk constantly until the sauce has thickened enough to coat the back of a spoon and has increased in volume.

Step 5

Remove the bowl from the heat and slowly pour in the clarified butter in a steady stream, whisking continuously, until the mixture is thick and smooth. Fold in the tarragon leaves and season, to taste, with salt and freshly ground black pepper.