Preheat oven to 150C/130C fan-forced. Grease 2 large baking trays. Line with baking paper.
Using an electric mixer, beat butter, caster sugar and vanilla until light and fluffy. Sift flours, cocoa and 1/4 cup icing sugar into a bowl. Gradually add flour mixture to butter mixture, beating until combined.
Turn dough onto a lightly floured surface. Knead until just smooth. Roll out dough between 2 sheets of baking paper until 5mm thick. Using a 5cm cutter, cut 30 shapes from dough, re-rolling scraps. Place shapes, 2cm apart, on prepared trays. Refrigerate for 15 minutes or until firm.
Bake for 18-20 minutes or until biscuits are just firm to touch, swapping position of trays halfway through cooking. Stand on trays for 5 minutes. Transfer to a wire rack to cool completely.
Sift remaining icing sugar into a bowl. Add 1 tablespoon cold water. Stir until a smooth, spreadable paste forms, adding more water if necessary. Spoon icing into a snap-lock bag. Snip off 1 corner. Leaving a 5mm border around edges, pipe icing over biscuits to cover. Set aside for 20 minutes or until set.