Prepare the cake batter: Whisk together the flour, baking powder, and salt in a medium bowl.
In a separate bowl, cream the butter and sugar
To make it easier: use an electric mixer and mix until light and fluffy, about 3–4 minutes. Add eggs one at a time, beating well after each addition, and mix in the vanilla extract.
Combine wet and dry ingredients: With the mixer on low, add the dry ingredients in three additions, alternating with the milk (start and end with the flour mixture). Mix just until combined, being careful not to overbeat.
Bake the sponge: Spread the batter evenly into the prepared pan and bake for 18–20 minutes, or until a skewer comes out clean. Cool in the pan for 20 minutes
Remove and cool fully on a wire rack.
Cut and prepare for dipping: Once cooled, cut the sponge into 2-inch squares. Place a wire rack over a tray to catch drips.
Make the icing: Sift the powdered sugar and cocoa into a bowl. Stir in the melted butter, then add boiling water a little at a time, whisking until smooth and glossy. Keep the icing slightly warm for easy dipping.
Coat the lamingtons: Using two forks, dip each sponge square into the chocolate icing, letting excess drip off, then roll in desiccated coconut until well coated. Place on the wire rack to set.
Optional filling: For jam-filled lamingtons, slice each sponge square in half horizontally, spread with raspberry or strawberry jam, then dip and coat as usual.