This herbal cousin of hollandaise was named after the birthplace of Henri IV, Béarn, an historic, former French province in Southwest France. The principal herb and flavor of the sauce is tarragon.
12tablespoons (¾cup; 1½sticks) butter
1tablespoon finely chopped shallot or onion
1tablespoon freshly chopped tarragon leaves or half the amount dried
3egg yolks (save whites for another purpose)
Salt to taste
1½tablespoon freshly chopped tarragon leaves or half the amount dried
Place a skillet on the stove and add about ½inch of water. Bring this water to the simmering point—that is, until it bubbles gently.
Place the butter in a small saucepan and let butter melt over low heat. Do not let the butter bubble; just melt it.
Select a 1½- or 2-quart heavy saucepan and add the vinegar, shallots, and 1tablespoon chopped tarragon. Place over direct heat and cook slowly until most of the vinegar evaporates. Remove the saucepan from the heat and let stand until cool.
Set the saucepan in the simmering water.
Add the 3 egg yolks to the saucepan and then 2tablespoons of cold water. Now comes the critical part of this recipe. You must start by beating the egg yolks with a wire whisk and beat them well. Let the whisk move briskly all 1tablespoon chopped fresh tarragon or half the amount dried around the saucepan, back and forth and in a circular motion. Continue beating until the eggs become frothy and slightly thickened. The eggs when ready will be yellow and custard-like and still somewhat frothy. This will require only 1 or 2 minutes.
Immediately remove the saucepan from the skillet and place saucepan on the table. Start adding the melted butter while beating vigorously with the whisk, back and forth and in a circular motion. Continue beating until all the butter is added. Add salt to taste, lemon juice, cayenne pepper, and the chopped tarragon leaves and beat. The sauce may be heated very gently by returning the saucepan to the skillet, but the sauce must be stirred constantly with the whisk.