Béarnaise sauce is an egg-yolk and butter emulsion in the Hollandaise family of sauces.
30 ml (2 tablespoons) tarragon vinegar
30 ml (2 tablespoons) sherry vinegar or dry white wine
1 shallot, finely chopped
2 egg yolks
75–100 g (⅓–½ cup / 3–4 oz) melted butter (warm but not hot)
Salt
Cayenne pepper to taste
1 tablespoon freshly-chopped tarragon
1 tablespoon freshly-chopped parsley
Put the vinegars, shallot, and herbs in a small saucepan; simmer until reduced to 1 tablespoon. This is the flavorful glaze. Strain and set aside to cool.
Add the egg yolks and whisk until the ribbon stage with a balloon whisk.
Place the bowl over a pan of hot water (a double boiler) and continue whisking. Gradually add the melted butter, whisking until the sauce thickens and all the butter has been added.
Season and serve.