Blend the butter, sugar and vanilla extract in a food processor. Add the flour, cocoa powder, whole egg and yolk. Blend again until the mixture forms a ball. Knead the dough lightly until it is smooth. Wrap and chill for 30 minutes.
Roll out the dough between 2 sheets of baking paper until it is 2.5 mm (⅛ inch) thick. Cut out 15 hearts using a 5 cm (2 inch) cutter. Reroll the trimmings and cut out 3 more heart shapes. Leave the hearts on the baking paper and slide the paper on to 2 firm baking sheets.
Bake in a preheated oven, 180°C (350°F), Gas Mark 4, for 10–12 minutes until the biscuits are firm and golden. Cool for 5 minutes, then transfer to a wire rack to cool completely.
Sift the icing sugar into a bowl, add 1 tablespoon cold water, stir and add another 1 tablespoon water to make a smooth piping consistency. Put into a piping bag with a fine plain nozzle and pipe various designs around the edges of the cookies.