Preheat your oven to 350°F. Grease the bottom and sides of a 9x13 inch baking pan and line with parchment paper. Set aside.
Make the vanilla sheet cake: In a medium sized bowl, combine flour, baking powder, and salt. Whisk to incorporate, and set aside.
In a large bowl, combine butter and sugar. Using an electric mixer fitted with the beater attachment or a wooden spoon, cream together butter and sugar until light and fluffy (about 2 to 3 minutes with an electric mixer set to medium speed, or 5 minutes by hand).
Add your eggs to the butter/sugar mixture one at a time, whisking well after each addition to combine. Pour in your milk and vanilla, and mix to combine. The mixture may be grainy, but that's perfectly fine!
Add the dry ingredients to the butter mixture. Fold together until just combined. Take care not to over mix!
Pour the cake batter into your prepared 9x13 inch baking pan, and spread into an even layer. Bake in the center of your preheated 350°F oven for 20 to 25 minutes, or until golden brown on top and a skewer inserted into the center comes out clean.
Cool the cake for about 10 minutes in the pan, then turn onto a wire rack, peel off the parchment paper, and set aside to cool completely to room temperature.
Place your cooled cake onto a large cutting board and cut into 32 squares. Pop the cake cubes into your fridge or freezer and chill until firm (about 2 hours in the fridge or 1 hour in the freezer).
Make the chocolate glaze: In a large bowl, combine powdered sugar, cocoa powder, and chocolate. Mix to combine.
Pour ½ a cup of boiling water into the powdered sugar mixture, and whisk until the chocolate is melted and you have a smooth glaze that's about the consistency of maple syrup. If your glaze is too thick, gradually mix in more boiling water, 1 tablespoon at a time, until it reaches the right consistency.
Coating: Line a large baking sheet with parchment paper, and set aside.
Pour your coconut into a shallow bowl or plate with high sides. I also like to pour the chocolate glaze into a small bowl to make dipping easier.
Using 2 forks, dip a chilled cake cube in the chocolate glaze. Toss to coat all sides, and allow any excess to drip off. Transfer the chocolate dipped cake to the coconut plate, and toss to coat all sides in coconut.
Place the coated cake onto the parchment lined baking sheet, and repeat the coating process with the remaining cakes. You can serve the lamingtons right away, but they're easier and less messy to eat once they've sat for about an hour for the glaze to set!