Combine all ingredients for the reduction in a saucepan and cook until the liquid has evaporated.
Place a bowl over a bain-marie and whisk the egg yolks together with the water and the reduction.
Whisk continually until the mixture is thickened and it forms a ribbon. Do not overcook the yolks or they will lose their ability to emulsify the sauce.
Keep whisking while gradually adding warm clarified butter into the bowl.
Remove from the heat, season to taste and pass the sauce through a sieve.
Add the freshly chopped tarragon and chervil to the béarnaise.
Notes
The reduction has a very intense vinegar smell because of the base mixture which is made by cooking herbs and other ingredients in a liquid until complete evaporation.