Preheat oven to 180oC. Grease 18 holes of two 12-hole mini muffin pans or line with mini patty cases.
Using an electric mixer, beat butter and caster sugar in a bowl until pale and creamy. Add egg and beat to combine. Combine flour, baking powder and coconut in a bowl. Stir into butter mixture alternately with the milk. Mix until just combined. Divide mixture between muffin holes.
Bake for 12 to 16 minutes or until golden brown and a skewer inserted into one cake comes out clean. Stand cakes in pan for 5 mintues before turning out onto a wire rack to cool.
To make the icing, beat the butter, icing sugar and milk until smooth and fluffy. Spread over cake tops. Sprinkle with coconut or alternatively, press coconut into icing to create a coconut coating.