Beat the butter and 3/4 cup of the sugar until light and fluffy.
Add the egg yolks beating well and scraping the bowl.
Beat in the vanilla, coconut, coconut milk and lime zest
In a separate bowl, sift the flour with the baking powder and salt.
With a wooden spoon, mix the flour into the butter mixture stirring gently (the batter will be quite thick).
In a separate bowl, beat the egg whites with the cream of tartar and remaining sugar until they form soft peaks.
Gently fold the whipped egg whites into the bake batter until combined.
Add the batter evenly into the prepared pans and bake 25-30 minutes or until a cake tester comes out clean.
Cool the cakes in the pan for 20 minutes before turning onto a cooling rack until completely cool.
For the buttercream:
Beat the butter until light and fluffy.
Mix in 2 cups of the sugar. Followed by the coconut milk. If the icing is too thin, add more sugar until it's the desired consistency.
Place the first cake layer onto a cake plate and spread a thick layer over top. Place the second layer on top and cover both layers evenly with the remaining icing.
Coat the cake with the shredded coconut and serve.