Strip the leaves from the tarragon and put to one side. Roughly chop the stalks, and place in a saucepan with the vinegar. Boil until there's just a tbsp of vinegar left, strain and set to one side.
Melt the butter in a pan over a low heat, or in a bowl in the microwave. Keep an eye on it so that it doesn't burn or overheat. Keep warm for the next stage.
Put the yolks into the processor bowl, then season with the cayenne and salt and pepper. Add a splash of the vinegar, then about a tbsp on the hot butter. Blitz, and then keep doing that, adding about 2 tbsp for the second round, 4 for the third etc, until the butter has all been added and the sauce is smooth and thick. Add the leaves and the rest of the vinegar and blitz again. If it's too think, use a little boiling water to thin, adding it and blitzing for a final go. Enjoy.