Grease a 9-inch (23cm) square cake pan and preheat the oven to 350°F (175°C).

In a large mixing bowl, cream the softened butter and granulated sugar together with an electric mixer on medium speed for 3-4 minutes until pale, light, and fluffy.

Add the eggs one at a time, beating well after each addition until fully incorporated. Add the vanilla extract and mix until combined.

In a separate bowl, whisk together the flour and baking powder. Add the flour mixture to the butter mixture in three additions, alternating with the milk in two additions, beginning and ending with the flour. Mix on low speed after each addition until just combined — do not overmix or the sponge will be tough.

Transfer the batter into the cake pan and bake for 30-35 minutes or until a toothpick inserted at the center emerges clean.

Remove the cake from the oven and let it cool in the pan for 10 minutes. Turn it out onto a wire cooling rack and let it cool completely, then refrigerate for at least 1 hour (or overnight) before cutting. A chilled sponge is much easier to cut and dip without crumbling.

Using a sharp knife, trim the edges of the cake if uneven, then cut into 16 roughly equal squares (about 2 inches / 5cm each).

Combine powdered sugar, cocoa powder, whole milk, melted butter, and vanilla extract in a medium mixing bowl. Whisk until a smooth mixture forms.

Using two forks, dip each cake square into the chocolate mixture, turning to coat all sides and letting excess drip off for a few seconds. Transfer immediately to the dish of desiccated coconut and roll gently, pressing lightly so the coconut adheres evenly. If the chocolate coating begins to thicken as you work, add whole milk one teaspoon at a time and whisk until it reaches a thin, pourable consistency again.

Place the coated lamingtons on a wire rack set over a baking tray (to catch drips) and let them set at room temperature for at least 1 hour before serving.