Beat the egg yolks lightly in a small bowl. Lightly crush the peppercorns and place them in a pan with the shallots and vinegar. Reduce by half and add the stock and strain on to the yolks, mix well.
Place the bowl over a pan of hot water, taking care the water does not touch the bottom of the bowl. Whisk continuously until the eggs thicken. Beat in the butter gradually. Do not allow the sauce to get too warm. Remove it from the heat occasionally so that the sauce remains only warm.
When all the butter has been added, finally add the tarragon and season to taste