Preheat oven to 180°C/160°C fan-forced. Line a large baking tray with baking paper.
Using an electric mixer, beat egg, sugar and orange rind until thick and pale. Sift over flour and baking powder. Add pistachios and apricots. Stir to combine. Turn out onto a lightly floured surface. Knead lightly until smooth. Shape into a 20cm long log. Place on prepared tray. Flatten slightly.
Bake for 30 minutes or until golden. Cool on tray for 15 minutes. Reduce oven to 140°C/120°C fan-forced. Using a serrated knife, slice log diagonally into 5mm-thick slices. Discard ends.
Place slices, in a single layer, on baking tray. Bake for 20 to 25 minutes, turning halfway through cooking, or until dry and crisp. Stand on tray for 5 minutes. Transfer to a wire rack to cool. Serve lightly dusted with icing sugar.