Preheat the oven to gas mark 4 or 180 degrees and line two trays with baking paper.
Beat together the butter and icing sugar until light and fluffy, then add the vanilla extract.
Gradually add the cornflour and plain flour and mix.
Fill a piping bag (with a star-shaped nozzle) with the mixture.
Pipe a zigzag of the mixture onto the tray, leaving a little space between each biscuit.
Bake for approximately 15 minutes until they are pale golden brown in colour.
Once the biscuits are cool, melt the chocolate.
Dip the tip of each biscuit in the chocolate, then place them back on the baking tray to dry. As you run out of chocolate, you may wish to use a teaspoon to drizzle the chocolate onto the remaining biscuits.