Preheat the oven to 180ºC/350F and greaseproof a bundt tin.
Place the butter and sugar into a bowl and combined until smooth. Add in the egg yolks and combine until well mixed.
Add the coconut milk and desiccated coconut, folding through the mixture until combined.
Sift the flour, baking soda and baking powder and add to the mixture, folding to combine.
Beat the egg whites until soft peaks form and fold the coconut mixture into the egg whites.
Spoon into the prepared cake tin and tap a few times to release any air bubbles.
Place in the oven and bake for 35 minutes or until a skewer comes out clean.
Remove and allow to cool for 5 minutes before turning out onto a cooling rack. Allow to cool completely.
Place the confectioner’s sugar, butter, lemon curd and milk into a bowl and beat to combine. Place in a microwave to heat through for approximately 7 seconds, stirring to melt the butter and bind the mixture.
Spread over the cake and allow to set for 5 minutes.