Simmer the shallot, tarragon sprig, chervil sprig, peppercorns and salt in the vinegar over low heat until the vinegar has been reduced by two thirds. Cool to lukewarm.
Add the egg yolks and beat briskly with a wire whisk. Place over low heat and gradually add the butter. Whisk until the sauce thickens. Strain. Season with cayenne and stir in the minced tarragon and chervil.