Preheat oven to 180°C/160°C fan-forced. Grease a 20cm x 30cm lamington pan. Line with baking paper extending paper 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 the plain flour, self-raising flour and cocoa powder. Add ½ cup coconut. Stir to combine. Spread mixture into prepared pan. Bake for 25 to 30 minutes or until firm to touch.
Make Chocolate icing: Sift icing sugar and cocoa powder into a medium heatproof bowl. Add butter and boiling water. Stir until smooth.
Spread hot slice with icing. Sprinkle with remaining ¼ cup coconut. Set aside to cool completely in pan. Cut into pieces. Serve.
