Put the vinegar, white wine, peppercorns and shallot into a small saucepan and bring to a gentle boil. Simmer until the amount of liquid has reduced by half.
Take the peppercorns out with a slotted spoon, then pour the mixture into a heat-proof bowl. This bowl needs to fit inside one of your saucepans. Allow the liquid to cool a bit so that when you add the eggs they don’t curdle.
Add the egg yolks to the bowl and whisk well.
Place the bowl over a pan of simmering water and whisk the sauce until it has thickened and is light in colour. This may take some time so be patient!
Melt the butter. I usually do this in the microwave but be careful because it melts very quickly and will explode all over your microwave if you do it for too long! Once it’s melted gradually add it to the sauce, whisking constantly.
Season with salt and freshly ground black pepper and add the chopped tarragon leaves.
Turn off the heat and leave the bowl over the pan until you are ready to use the sauce.