Cut butter into thirds; bring it to room temperature. In a small saucepan combine vinegar, green onion, tarragon, chervil, and pepper. Bring to boiling; boil, uncovered, on high for 2 minutes or until reduced by about half.
In the top of a double boiler combine vinegar mixture, egg yolks, and water. Add a piece of the butter. Place over boiling water (upper pan should not touch water). Cook, stirring rapidly with a whisk, until butter melts and sauce begins to thicken. Add the remaining butter, a piece at a time, stirring constantly until melted. Continue to cook and stir until sauce is thickened (1 to 2 minutes more). Immediately remove saucepan from heat. If sauce is too thick or curdles, immediately whisk in 1 to 2 tablespoons hot water. Serve with beef, pork, or poultry. Makes 3/4 cup sauce (twelve, 1-tablespoon servings).