Heat oven to 170°C. Grease and flour a bundt cake pan.
Beat butter, sugar, baking powder, vanilla in a large bowl with a mixer until fluffy.
Add the eggs, 1 at a time, beating well after each.
On low speed, beat in the flour gradually, alternating it with the milk.
Spoon about ⅓ of the batter to another bowl. Add the cocoa powder or melted chocolate and combine.
Stir the coconut into the remaining batter. Spoon half the coconut batter into the pan.
Drop spoonfuls of the chocolate batter on top leaving spaces between each dollop. Drop spoonfuls coconut batter between chocolate batter. Repeat this process (alternating batters) with the rest of the batter.
Put the pan into the oven and bake for about 55 minutes or until a skewer inserted in the center of the cake comes out clean.
Cool in the pan for 10 minutes then invert the cake onto the rack to cool completely.
Mix some coconut milk with icing sugar. Brush the cake with this and scatter shredded coconut on top. Let it set and serve.