Beat the butter and sugar together in a mixing bowl. Add the lime rind, egg and coconut and beat until smooth. Gradually beat in the flour.
Spoon the mixture on to a piece of greaseproof paper and shape into a log about 35 cm (14 inches) long. Roll the dough in the chopped pistachios then wrap in the paper and twist the ends together. Chill in the refrigerator for at least 15 minutes or up to 3 days.
To serve, unwrap and slice off as many biscuits as required. Arrange on a greased baking sheet and bake in a preheated oven, 180°C (350°F), Gas Mark 4, for 8–10 minutes until pale golden. Leave to cool for 5 minutes then transfer to a wire rack to cool completely. These are best eaten on the day they are made.