Mix the flour, sugar, salt and cocoa in a bowl. Add the butter, egg and juice. Knead by hand to create a soft, smooth dough. Cover the dough and chill for approx. 30 mins.
Divide the dough into 4 portions. Roll out each portion to a roll approx. 40 cm long. Cut each roll into 5 pieces. Roll the pieces out a little thinner on one side. Flatten the other side a little. Transfer the icicles to a baking tray lined with baking paper.
Approx. 10 mins. in the centre of an oven preheated to 180°C.
Stir everything together in a tall glass. Dip the icicles in the glaze. Hold the icicles the other way round so that the glaze trickles down. Dry on a rack.