Preheat your oven to 175°C (350°F). Grease and line a square tray (48 x 220 x 230mm) with baking paper.
In a bowl, cream the butter and sugar together until pale and fluffy (about 2–3 minutes with an electric mixer or whisk).
Add the egg and beat until fully combined. Mix in the vanilla extract.
In a separate bowl, whisk together the flour, baking powder, baking soda, and salt.
Alternate adding the dry ingredients and milk to the wet mixture. Begin and end with dry ingredients, mixing gently until just combined. The batter should be smooth.
Pour the batter into the prepared tray and smooth out the top.
Bake for 18–20 minutes, or until a skewer inserted into the centre comes out clean. The top should be lightly golden.
Cool the cake completely in the tray before cutting into squares. (This step is very important.)
Make the icing: In a bowl, mix the sifted icing sugar and cocoa powder. Add the melted butter, milk, hot water, and vanilla extract. Stir until smooth. The consistency should be pourable but slightly thickened.
Pour the desiccated coconut onto a shallow plate or dish.
Cut the cooled cake into small squares (3–4 cm is ideal). Trim the edges for neatness, if needed.
Dip each square into the chocolate icing for a few seconds, making sure all sides are well coated.
Roll each chocolate-coated piece in the coconut until fully covered.
Place the finished Lamingtons on a baking tray lined with parchment paper to set. Let them rest until the icing is dry, this usually takes a few hours. For best results, let them sit overnight if you’re making them in the afternoon or evening.