Before you start, preheat oven to 170°C. Grease and line a baking tray (about 20 x 20cm) making sure the baking paper comes up the edges.
In a large bowl or bowl of your stand mixer, place sugar, eggs and vanilla. Use electric beaters to beat until pale, about 4 minutes. Meanwhile, melt butter in a medium pot or in the microwave.
Add flour, baking powder and butter to bowl with eggs and whisk in gently. Do not overmix.
Transfer mixture to prepared pan and give it a few taps on the bench to ensure it is level. Bake for 25-30 minutes, until golden on top and cooked through. A knife inserted will come out clean. Set aside to cool on a cooling rack.
While cake cools, make icing. Add all icing ingredients to a large bowl and whisk to combine. Add a few tablespoons of boiling water to thin out, if needed. Place coconut in a separate bowl.
Cut cake into 16-20 even squares.
Keeping one hand for the wet mixture and one hand for the dry, dunk each piece of sponge first into icing and then into coconut.
To finish, cut a slice into the lamingtons, fill with some jam then serve.