Preheat your oven to 350°F (175°C). Grease and line an 8-inch square baking pan with parchment paper.
In a medium bowl, sift together the flour, baking powder, and salt. Set aside.
In a large mixing bowl, beat the softened butter and granulated sugar together until light and fluffy. Add the eggs one at a time, beating well after each addition. Stir in the vanilla extract.
Gradually add the flour mixture to the butter mixture, alternating with the milk, beginning and ending with the flour mixture. Mix until just combined.
Pour the batter into the prepared baking pan and smooth the top. Bake in the preheated oven for about 25-30 minutes, or until a toothpick inserted into the center comes out clean.
Allow the cake to cool in the pan for 10 minutes, then transfer to a wire rack to cool completely. Once cooled, cut the cake into 16 squares.
In a medium bowl, sift together the powdered sugar and cocoa powder.
Add the milk and melted butter, and stir until smooth and well combined.
Place the desiccated coconut in a shallow dish.
Dip each cake square into the chocolate icing, making sure to coat all sides. Allow any excess icing to drip off.
Roll the chocolate-coated cake square in the desiccated coconut, pressing gently to adhere. Place the coated lamingtons on a wire rack to set.
Allow the lamingtons to set for about 30 minutes before serving. They can be stored in an airtight container at room temperature for several days.
Enjoy your meal!