Beat the cream cheese and whipping cream to a smooth consistency. Then beat in the Kahlua.
Cut sponge cake into half. Brush the top of the sponge with the coffee and brandy mixture. Repeat with the other half until coffee is used up.
Lay one piece of the soaked sponge cake on a flat, rectangular tray and top with half the cream cheese mixture. Sprinkle on half the coconut flakes. Top this with the other piece of sponge cake, spread on the rest of the cream cheese mixture and sprinkle on the coconut flakes.
Dust with the icing sugar and cocoa powder. Refrigerate the cake for at least an hour, preferably overnight. Serve with some chocolate shavings, if liked.