Combine half the bunch of tarragon, the shallots, peppercorns, vinegar and wine in a small saucepan and bring to a boil. Reduce to a simmer and simmer until it has reduced by half. Let the mixture cool and strain through a fine strainer.

Combine the tarragon reduction, egg yolks, and salt in a blender jar. Blend until well mixed.

Slowly drizzle in the melted butter.

Season with salt and cayenne pepper. Add the leaves from the remaining half bunch of tarragon and buzz in the blender a couple of times. Hold the Béarnaise in a bowl covered with plastic wrap, over a barely simmering water bath.