In a medium saucepan, add shallots, white wine, white wine vinegar, tarragon and peppercorns; stir well. Bring the mixture to a boil, reduce the heat to medium and simmer until it reduces to about 3 to 4 tbsp., about 15 minutes.
Remove from the heat and strain the mixture through a fine sieve sitting over a small bowl, pressing on the solids to extract as much liquid as possible; set aside.
SAUCE
In another medium saucepan, add yolks and whisk very well until they get thick, about 1 minute.
While whisking, pour in the white wine reduction.
Set the heat to medium and season a little bit with salt. While whisking constantly, keep lifting the saucepan off the heat - the trick here is to not shock the yolks by gradually heating them up.
When the custard gets thick, move the saucepan away from the heat and whisking continuously, start adding the melted butter, pouring in a few drops at first – remember don’t shock the yolks! Gradually add more until it’s all incorporated.
Add lemon juice and fresh chopped tarragon; whisk into the mixture. Taste and adjust the seasoning if needed. If the sauce gets too thick, add about half a tablespoon of lukewarm water to thin it out.
If not using it right away, move to the back burner, keeping the sauce warm on very low temperature. To prevent skin formation, place a piece of wax paper on top, making sure it touches the surface.
Notes
Footnote: If the sauce is too thick, add a little bit of lukewarm water to thin it out while whisking constantly.