Preheat oven to 160C. Prepare a lamington pan (about 33cm x 27cm x 6.5cm) by lining with greaseproof paper.
Beat eggs with sugar until soft peaks form.
Fold in sifted flour and add melted butter.
Pour mixture into prepared pan. Smooth top.
Bake for one hour at 160C,until a skewer inserted in the centre comes out clean.
Remove sponge from oven and let cool.
Trim all sides to remove crust,and cut into 5cm cubes.
Mix together sugar,matcha powder and water in a medium saucepan over medium heat until sugar dissolves.
Dip sponge cubes quickly on all sides,let excess drip back into saucepan,and roll in the desiccated coconut. Place on a wire rack over a baking tray to set.
Note: Lamingtons can be stored in the fridge for two days.