Set the oven to 180°C/350°F, or 160°C/320°F for a fan-forced oven. Let it reach temperature before the batter goes in.

Pass the flour and baking powder through a sieve into a bowl. The dry mixture should look even and free of visible lumps.

Grease a 20 cm x 30 cm / 8 inch x 12 inch cake pan and fit it with parchment extending above all four sides. The exposed paper will provide handles for lifting the baked cake.

Work the butter, sugar, and vanilla with an electric mixer at medium-high speed for about 1 1/2 to 2 minutes. Stop when the mixture looks paler, aerated, and fluffy.

Beat in each egg separately, fully incorporating it before adding the next. A smooth mixture, rather than a grainy or separated one, is the target.

Fold in half the flour mixture, stir in half the milk, then repeat with the remaining flour and milk. Finish with an evenly combined batter and avoid unnecessary mixing.

Transfer the batter to the lined pan and bake for 25 minutes. A skewer pushed into the center should emerge clean.

Leave the cake in its pan for 5 minutes, then lift it by the parchment handles and transfer it to a wire rack. Allow it to cool completely before cutting.

Divide the cooled cake into a 5-by-3 grid for 15 squares, or cut 18 rectangles, and freeze the pieces for 1 to 1.5 hours. The cut sponge should feel firm enough to maneuver without compressing.

Stir the powdered sugar, cocoa, butter, and boiling water together in a heatproof bowl. A smooth, syrupy glaze is ready for dipping; it should not flow like plain water.

Spread the coconut across a broad, shallow bowl or pan. Leave enough exposed surface to turn each cake piece comfortably.

Turn a sponge piece through the icing with two forks, then move it into the coconut, coat every face promptly, and place it on a tray. The finished piece should have an even coconut covering with no large bare patches.

Coat the remaining cake pieces in the same sequence. Use the forks to support the sponge rather than squeeze it.

Leave the coated cakes undisturbed for 1 to 2 hours, until the icing sets. The coating should cling to the cake instead of smearing readily.

Whip the cream with the white sugar until it holds firm peaks. The peaks should keep their shape when the beaters lift away.

Slice each set lamington horizontally, spread jam over the bottom, pipe or spoon on cream, replace the top, and refrigerate. The filling should hold between the layers without flowing out.