Preheat oven to 180°C. Lightly grease an 18 x 28 cm slim pan. Line base and sides with baking paper, extending paper 2 cm above edge of pan.
In a large bowl, combine butter, sugar and egg. Sift flours and cocoa together into the bowl, and mix lightly until combined. Fold coconut through. Spread mixture into prepared pan, smoothing top.
Bake 20-25 minutes, until firm. Let cool completely in pan.
Make icing: in a medium bowl, combine icing sugar, cocoa and butter. Stir in enough hot water so the icing is spreadable. Spread icing over the cooled slice. Sprinkle with toasted coconut. Serve slice cut into squares.