Preheat oven to 180 degrees Celsius Grease a 20cm x 30cm lamington pan. Line with baking paper extending 2cm from edge of pan at long ends.
Place butter, brown sugar, egg and vanilla in a large bowl. Stir until well combined. Sift over flours and cocoa. Add 1/2 cup cocounut. Stir to combine. Spread mixture into prepared pan. Bake 25 - 30 minutes or until firm to touch.
Make Chocolate Icing: Sift icing sugar and cocoa into a medium heat proof bowl. Add butter and boiling water. Stir until smooth.
Spreas hot slice with icing. Sprinkle with remaining coconut. Set aside to cool completely in pan. Cut into pieces and serve.