Lightly grease and line the bases of 3 x 20cm cake tins.
For the sponge, whisk the butter and castor sugar until light and pale.
Gradually beat in the eggs, mixing well after each addition.
Sift the flour and baking powder into the mixture and fold in the coconut until thoroughly incorporated. If the mixture seems too thick, add a few tablespoons of milk.
Lastly, fold in the lime zest and juice.
Divide the mixture evenly between the 3 cake tins and bake for 20 minutes or until springy.
Allow the cakes to cool slightly, then remove them from the tins to cool completely.
For the icing, beat the butter, cream cheese, coconut, and vanilla until smooth, then gradually add the icing sugar until well incorporated. Lastly, mix in the lime juice and zest.
To assemble the cake, spread some of the icing on top of the base cake layer then top with the next layer and repeat with the remaining layer. Cover the whole cake with the icing and smooth it with a palette knife.
Gently press the toasted coconut onto the sides of the cake and top with a sprinkling of lime zest.