Put water, white wine vinegar, onion, chopped estragon stalk, salt and pepper into a saucepan and cook it until under half of the liquid is left.Let it cool a little and use a sieve to get a nice clear essence.
Meanwhile melt the butter in another pot at low temperature. Use only the clarified butter after it all has melted.
Heat the essence and egg yolks in a saucepan (or water bath) at very low heat and during constant whipping.Let the eggs thicken while whipping well. It takes about 2-3 min.
Start by adding 1 tablespoon of butter while still whipping constantly. Then add one more and so on. Finally you will be able to add the butter in a thin stream while whipping.
When the sauce is thick and fine, add the estragon, chervil, salt and pepper. Season with lemon if you want to
If the sauce gets a bit too thick put in some cold water during constant whipping.Serve immediately.