Lamingtons: Preheat your oven to 350 degrees F (180 degrees C). Butter, or spray with a nonstick cooking spray, the bottom and sides of an 8 inch (20 cm) square cake pan. Then line the bottom of the pan with parchment paper.

In a large bowl sift or whisk together the flour, baking powder, and salt.

In the bowl of your electric mixer, or with a hand mixer, beat the butter until soft. Add the sugar and beat until light and fluffy (about 2-3 minutes). Add eggs, one at a time, beating well after each addition. Scrape down the sides of the bowl as needed. Add the vanilla extract and beat until combined. With the mixer on low speed, alternately add the flour mixture (in three additions) and milk (in two additions), beginning and ending with the flour.  

Spread the batter into your pan and smooth the top with the back of a spoon or an offset spatula. Bake in preheated oven for about 20 - 25 minutes, or until a toothpick inserted in the center of the cake just comes out clean.

Cool the cake in the pan, placed on a wire rack, for about 10 minutes. Then place a wire rack on top of the cake pan and invert, lifting off the pan. Remove the parchment paper and then turn the cake right side up. Once the cake has completely cooled cut into 16 - two-inch (5 cm) squares.

Chocolate Frosting: Place the powdered sugar, cocoa powder, butter and milk in a heatproof bowl placed over a saucepan of simmering water. Stir the mixture until it becomes smooth and of pouring consistency.

To assemble Lamingtons: Place the coconut on a large plate. One at a time, dip the squares of cake into the chocolate frosting and then roll the cakes in the coconut. Gently transfer the Lamingtons to a clean wire rack to set. (If the icing becomes too thick, simply place the frosting back over the simmering water and reheat until it is of pouring consistency. You may have to do this a few times as the frosting has a tendency to thicken over time. Add a little more milk to frosting if necessary.)

Once the Lamingtons have set, store in an airtight container for several days.

(Alternatively, you can place the squares of cake on a wire rack that is placed on a large baking sheet. Then pour the frosting over the top of each cake, letting it drip down the sides. Some of the frosting may drip onto the baking pan. Pour this frosting back in your bowl and reuse (strain if necessary). 

Makes 16 2-inch (5 cm) Lamingtons.