Place egg yolk, vinegar, water and a pinch of salt in a small mixing bowl and place this over a pan of simmering water. Whisk everything in the bowl together and keep whisking it over the simmering water until the mixture thickens. This has now stabilised the base for your emulsion sauce. Remove the bowl from the pan and turn off the heat.
Without working over heat, slowly whisk in the nicely warm (but not too hot) melted butter until it’s all used up.
Season the velvety, buttery sauce with a little lemon juice, a pinch of cayenne pepper, the chopped tarragon and more salt if required. This sauce will not keep, once it is made you need to keep it warm and use it all up.