In a metal bowl place egg yolks and beat together, add tarragon. Put over boiling water or double boiler and let water simmer, not too hot.
Whip with whisk constantly and add butter chopped into little cubes one at a time until all are melted in and combined.
Have a cold water bath ready to stick metal bowl in if butter and egg begin to separate. Add one of the ice cubes to mixture and continue beating until you see it come together again. Once it is back to normal return to adding butter until all is used up.