Melt the butter, then turn the heat to low and let all the water cook out. You will be left with butterfat and butter solids. Transfer the butter into another container to cool.

Add the vinegar to a pot and bring to just under a simmer. Add 10 g tarragon to the bottle, then add warm vinegar to the bottle. Let this come to room temperature before adding the cap. Let this sit for one week to become full-flavored.

To a pan, add the white wine, white wine vinegar, shallots, tarragon, and a large crack of black pepper. Bring to a low simmer, cooking for 10-15 minutes or until reduced by half.

Strain the reduction through a fine chinois and reserve until needed.

Combine the egg yolks with two teaspoons of reduction in a bowl over a water bath. Whisk the mixture until it becomes light and frothy. You will know that it is ready when the sabayon slowly comes back when you move it with a rubber spatula.

Slowly add in the butter, making sure that it is fully mixed in before adding the next amount. If the sauce starts to become too thick (it will look like mayo), add in some more reduction.

Once all the butter is added, taste the sauce to see if you need salt, pepper or more reduction. Right before using the sauce, add in the final chopped tarragon.