For the reduction, place all the ingredients in a small saucepan over a medium–high heat and reduce by two-thirds. Allow it to cool, then strain the reduction, discarding the peppercorns, shallot and tarragon, and place in a heatproof bowl.
Place the butter in a small saucepan and melt over low heat without stirring. As soon as the butter has melted, remove from the heat and set aside to cool for 5 minutes. Optimum temperature is 55–58°C.
Whisk the egg yolks into the reduction, then place the bowl over a saucepan of simmering water (ensure the water is not boiling and the base of the bowl does not touch the water) and, whisking continuously, slowly start pouring in a quarter of the hot butter. Continue whisking in the butter until the mixture begins to thicken, then take the bowl off the heat, place on a wet cloth on a work surface and continue adding the melted butter in a very slow, steady stream, whisking continuously and being careful to add only the butter and not the milk solids at the bottom of the saucepan (discard these). The sauce will thicken as the hot butter is added. Season with salt and black pepper, and add the tarragon and chervil.