1. Preheat the oven to 375 degrees F (190 degrees C). Grease and flour an 8x12-inch pan.

2. Make the cake: Sift flour, baking powder, and salt together into a bowl.

3. Beat sugar and butter in a large bowl with an electric mixer until light, fluffy, and noticeably lighter in color. Mix in one egg until fully incorporated; mix in remaining egg and vanilla. Add flour mixture in two batches, alternating with milk, beating until just incorporated after each addition. Pour into the prepared pan.

4. Bake in the preheated oven until a toothpick inserted into the center comes out clean, 30 to 40 minutes. Remove from the oven and let stand in the pan for 5 minutes, then turn out onto a wire rack and let cool completely, about 30 minutes.

5. Wrap cooled cake with plastic wrap. Place onto your counter at room temperature to let firm up, 8 hours to overnight.

6. When ready to finish the lamingtons, make the icing: Place confectioners' sugar and cocoa into a mixing bowl. Mix in warm milk and melted butter until icing is fluid but not too runny.

7. Unwrap the cake and cut into 24 squares. Cover a work surface with parchment or waxed paper, then set a wire rack over top. Pour coconut into a shallow bowl.

8. Using a fork, dip each cake square into icing, turn until all sides are coated, then roll in coconut. Place onto the rack to dry.

Tips

Desiccated coconut is slightly dried, ground coconut. It's not the same as sweetened, shredded coconut.