Place egg yolks in a tall narrow container that the blender stick fits in all the way to the base.
Add water, lemon juice, cayenne pepper and salt. Mix to combine.
Melt butter in a small saucepan. Spoon off much of the white as it melts.
With the blender stick on, slowly pour the butter in a thin stream into the eggs over around 45 seconds. Leave any of the white part of the butter that you couldn’t scrape off. (It won’t hurt if some manages to slip in.
Blend for a further 10 seconds, moving the stick up and down.
If too thick, mix in warm tap water 1 teaspoon at a time.
Taste for lemon level, adding a little more if desired, add the tarragon leaves and serve immediately. If you need to reheat do it in a small saucepan and heat slowly, if the sauce starts to separate (break) add a drop of water one at a tie until it comes back together.