Method

Put vinegar, shallot, lemon juice & half of the tarragon in a saucepan, heat & reduce liquid by half, sieve out bits & use a back of a spoon to remove all liquid, set aside in a jug to cool.

Melt butter in a saucepan or in a glass jug in a microwave oven until melted but not boiling.

In a metal or glass bowl whisk vinegar & egg yolk together.

Place a saucepan on the lowest heat possible, place the bowl on top of the hot water (water must NOT touch the bottom of the bowl, then with a whisk slowly add the melted butter into the bowl whisking hard all the time (if it curdles start again, but slower with the butter) until you have used all the butter.

Remove bowl off the saucepan, mix in the other half of the tarragon, salt & pepper.