Spread the coconut out on a small baking tray and place in the oven for 5 - 6minutes, until lightly toasted. Keep an eye on it as it can burn fairly quickly.
Line two large baking trays with greaseproof paper and set aside.
Put the sugar into a large mixing bowl along with the lime zest. Work the zest in to the sugar with the back of a tablespoon. The sugar will turn slightly green, become very fragrant and look slightly damp.
Add the butter and beat together with the lime sugar until pale and fluffy.
Add the flour, cornflour and cooled toasted coconut and fold into the butter mixture until it starts to come together. Tip the mixture out on to a lightly floured worktop and use your hands to work the dough into a smooth ball.
Flatten slightly, then with a floured rolling pin roll out until about 1cm thick.
Cut into slices and lay out on the prepared baking trays.
Fork the shortbread a few times then sprinkle with the untoasted coconut.
Chill for about 30 minutes.
Bake for 20 minutes until the edges are just lightly browned.
Allow to cool on the tray then transfer to a wire rack to cool.
Notes
Tip; For a crispy shortbread cook for a little longer until golden all over.