1In a small heavy saucepan, whisk the egg yolks and water. Cook and stir over low heat or simmering water until mixture bubbles around edges and reaches 160°, about 20 minutes.
Meanwhile, in a small saucepan, combine the wine or broth, vinegar, shallot, 1-1/2 teaspoons tarragon and peppercorns. Bring to a boil. Reduce heat; simmer, uncovered, for 10 minutes or until reduced to 2 tablespoons. Strain and set liquid aside.
Cut cold butter into eight pieces; add to egg yolk mixture, one piece at a time, stirring after each addition until melted. Stir reserved liquid and remaining tarragon into prepared sauce. Serve immediately.