Butter a dish or deep baking sheet/tin that's approx 11-12in x 7-8in (28-30cm x 18-20cm) and at least 1 in (2.5cm) deep. A 9x9in (23x23cm) square pan will also work. Line it with parchment paper, on the bottom and two longer sides, overhanging the sides slightly and pressing the paper gently into the butter to help it stick.
Mix together the flour, coconut, sugar and cocoa powder in a bowl. Lightly beat the egg and melt the butter. Add both and the vanilla to the dry ingredients and mix until well combined.
Put the mixture into the prepared dish and press it down evenly, flattening the top so it's smooth. Bake for approx 20-25 minutes until the firm and the top looks dry.
Towards the end of the baking time, prepare the frosting/icing. Sift the confectioner's sugar and cocoa powder together in a bowl. Add the melted butter and hot water and mix until well combined. Add a little extra sugar/water if needed to make a semi-thick but workable mixture.
Once the base is ready, top with the frosting while it is still hot. Try to spread evenly, right to the corners, but be aware if you try to work it too much the top will become less even. Once done, sprinkle with a little coconut while the frosting is still wet. Leave to cool/firm up before cutting into pieces.
To cut into pieces, it's easier to loosen the short edges of the slice and lift it out of the dish in one piece. Then, cut into whatever size pieces suits (for this size, I suggest 16 pieces).
Notes
Photographs show a half quantity, using a 7 ½ x 5 ½ in dish, but process is the same (everything is simply halved).