A classic flavour combination in a light & fluffy cake.
Preheat oven to 170C / 150C Fan / Gas 3.
Butter or line a 20cm loose-bottomed cake tin.
Sift together the flour, baking powder and salt. Set aside.
Put the butter, sugar & vanilla extract in a large bow and beat together until fluffy.
Beat in the eggs, one at a time, including 1 tablespoon of the flour mix each time.
Beat in the coconut milk with another tablespoon of the flour mix.
Fold in the desiccated coconut, lime zest (reserve a little for decoration), and the rest of the flour mix.
Transfer the cake mixture to the prepared tin and smooth the top.
Put in the oven and bake until a cocktail stick comes out clean (55-70 min).
Leave in the tin for 5 minutes, then turn out onto a wire rack and leave until completely cold.
Add the juice from one of the limes to the sifted icing sugar and mix well together: you need a thick but pourable icing, so add some of the juice from the second lime if necessary.
Pour the icing over the cake, letting it run down the sides.
Leave to set a few minutes before sprinkling over coconut shavings and reserved lime zest.
Cake will keep for 4 days in an airtight container.