In a food processor, blend the egg yolks, lemon juice and pepper. Beat until frothy and light in colour. Cut butter into small pieces and heat in the microwave until hot and bubbling. With the food processor running, add the melted butter very slowly – and keep blending until sauce is nice and thick. Add the tarragon and lemon zest. Pour the mixture into a metal bowl.
1/3 fill a saucepan with water and heat gently, place the metal bowl with the Hollandaise mixture on top of the saucepan and whisk continuously until sauce is thick and heated through. Serve over poached eggs or chicken.