Put the shallot, pepper, vinegar, chervil and tarragon in a saucepan and let it reduce on low heat.
During this time melt your butter being careful to remove the whey.
Place the back of he saucepan which contains the shallots in some cold water. Stir in the egg yolks. Heat in a bain–marie blending with a whisk at the same time until it takes a mayonnaise consistency. Next, fold in the melted butter.
Salt and add the last spoonfuls of tarragon and chervil.
Some cooks filter the sauce before adding fresh herbs.
The Bearnaise sauce is used to accompany fish and meat dishes.
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