Heat the oven to 180°C conventional or 160°C fan. Line a 20 cm square tin with baking parchment, leaving an overhang on two sides.
Combine the flour, brown sugar, 80 g coconut and 25 g cocoa in a mixing bowl. Break up any lumps of sugar.
Pour in 125 g melted butter and mix until evenly combined. Press firmly and evenly into the lined tin with the back of a spoon.
Bake for 18 to 22 minutes, until the edges are set and the centre feels just firm. Avoid overbaking. Leave in the tin on a rack until cool, about 45 minutes.
For the icing, mix the powdered sugar and 15 g cocoa. Add 20 g softened butter and the hot water a little at a time, stirring until smooth and spreadable. You may not need every drop.
Spread the icing over the cooled base. Sprinkle with the remaining 10 g coconut. Allow about 45 minutes for the icing to set, longer in a warm kitchen.
Lift out using the parchment and cut into 16 equal squares with a sharp knife. Wipe the blade between cuts for clean edges.