Dice the shallot.

Heat the olive oil in a small pan and glaze the shallot at medium fire for 5 minutes.

Add the vinegar, the wine, the tarragon and add the salt and pepper

Let simmer for 15 minutes with the lid on (low heat) and then increase the fire a bit and take the lid off to let the vinegar and alcohol cook off a little. Aim to keep 3.5 oz (100 g) liquid left

Strain through a small sieve and press with a spoon the shallot/tarragon mixture in the sieve to release all its juices. Let the gastrique cool to room temperature and reserve

Melt the ghee and heat the sunflower oil to approximately 120 F (50 C) (a brief time in the microwave oven works) and mix together

Bring egg yolks and gastrique to room temperature. Thereafter mix them in a stainless steel bowl with a whisk

Heat the bowl au bain marie under constant whisking. After a few minutes the temperature will approach 163 F (73 C) and the mixture will become thicker and more viscous. Continue whisking for a few tens of seconds, to whisk a lot of air in, but be careful not to over-heat.

Take the mixture off the heat source and place on a towel or something that insulates.

Under vigorous whisking start adding the oil, first drop wise, then in larger speed

The sauce becomes even thicker. Serve immediately