Place the butter into a small pot and bring to the boil. Then remove from the heat.
Add the tarragon vinegar, lemon juice, shallots and peppercorns into another small pot and bring to the boil, allow to reduce by half.
Place the egg yolks into a tall jug and add the water, add the vinegar/lemon juice reduction and using a hand blender, whisk the egg yolks and water together for at least 1 minute, allowing the colour to lighten.
With the whisk still running slowly add the melted butter until it is all combined. Continue to whisk for a further seconds. Check the sauce for seasoning and adjust accordingly.
Add the chopped tarragon and mix to combine.
Place the jug into a heat proof container and fill with just boiled water, to keep your sauce warm until ready to use.