Preheat oven to 180 degrees C. Line two baking trays with baking paper.
In a food processor, process flour, icing sugar and cocoa until combined. Add butter; process until mixture resembles fine breadcrumbs. Add egg; process until dough clings together.
Knead dough on a floured surface for 30 seconds. Mould into two disc shapes; cover and refrigerate for 1 hour. Roll out each piece of dough, between sheets of baking paper, to a 24cm x 12cm rectangle. Cut 6cm x 3cm rectangles from each pastry piece to make a total of 32 biscuits.
Place biscuits 3cm apart on prepared trays. Bake for 15 minutes or until golden. Allow to cool for 5 minutes before removing to wire racks to cool completely. Dip half of each biscuit in melted white chocolate; place on lined baking trays to set. When white chocolate is set, drizzle dark chocolate over white chocolate in a zig zag pattern. Allow to set.