Preheat the oven to 350 Degrees F. Place oven rack to middle position. Either butter or spray the bottom and sides with non-stick cooking spray of an 8-inch square baking dish; set aside.
In a large bowl, sift together the flour, baking powder, and salt; set aside.
In another bowl using your electric mixer, beat the butter until soft. Add the sugar and beat until light and fluffy. Add the eggs, one at a time, beating well after adding each egg addition. Add the vanilla extract to the mixture and mix well. Use a spatula to alternately mix in the sifted flour mixture and the milk, in three additions, beginning and ending with flour.
Spread the batter into the prepared cake dish and smooth the top with a spatula.
Bake approximately 25 to 30 minutes or until a toothpick inserted in the center of the cake comes out clean. Remove from oven. Let the cake cool in the baking dish for approximately 7 minutes and then invert it onto a wire rack to let cool.
Once the cake has cooled, cut it into 16 (2-inch squares) and wrap each square of cake in plastic wrap. Place the cake squares in the refrigerator for at least 2 hours (more is better). Hint: You can also freeze the cake squares. Frozen cake squares are much less crumbly when rolling in the runny icing. You have to work quickly though because they thaws fast.
To assemble the Lamingtons: Place some paper or plastic wrap under the wire racks to catch any dripping frosting. Place the cake squares on the racks and have your warm Chocolate Frosting and coconut ready. If the frosting starts to set while using, stand bowl in hot water until frosting thins down.
Quickly spoon or ladle the warm Chocolate Frosting over the chocolate squares, and then let the cake drain. Coat each cake square on all sides in the Chocolate Frosting. It is best to just do a few cake squares as a time.
Using a small knife or spatula, gently roll each coated cake square in the coconut. Repeat with remaining cake squares. Set the cakes aside to dry before serving.
Once the Lamingtons have set, store in an airtight container for several days.
Makes 16 (2-inch) Lamington squares.
Place the powdered sugar, cocoa powder, butter, and milk in a heat-proof bowl over a saucepan of simmering water. Stir the mixture until it is smooth and of pouring consistency. Remove from heat. You do not want the liquid to get too thin as the cake will not absorb the frosting properly.
* It is the white fleshy part of the coconut, which is processed into smaller shreds or flakes. After being cut or grounded into granules and/or slices, the coconut pieces are dried to remove maximum moisture from them. Available at most supermarkets.
Lamington Cake Recipe: https://whatscookingamerica.net/history/cakes/lamington.htm