01 - Preheat oven to 350°F. Grease an 8-inch square cake pan and line the bottom with parchment paper.
02 - Sift the flour, baking powder, and salt together into a medium bowl. Set aside.
03 - In a large mixing bowl, beat the softened butter and granulated sugar together using an electric mixer until pale, light, and fluffy, approximately 3 to 4 minutes.
04 - Add the eggs one at a time, beating well after each addition. Stir in the vanilla extract until evenly distributed.
05 - Gradually add the sifted flour mixture to the batter in two additions, alternating with the milk. Fold gently with a spatula until just combined, being careful not to overmix.
06 - Pour the batter into the prepared pan and smooth the top with a spatula. Bake for 22 to 25 minutes, or until a wooden skewer inserted into the center comes out clean.
07 - Allow the cake to cool in the pan for 10 minutes, then turn it out onto a wire rack to cool completely.
08 - Once fully cooled, trim any domed top if necessary and cut the cake into 12 even squares. Place the squares in the freezer for 30 minutes to firm up, which makes coating much easier.
09 - Gently warm the raspberry jam with the hot water in a saucepan over low heat, stirring until smooth and pourable. Transfer the mixture to a shallow bowl.
10 - Spread the desiccated coconut in a separate shallow bowl or plate. Arrange the coating station with the raspberry mixture, coconut, and a wire rack lined with parchment paper nearby.
11 - Working with one square at a time, dip each chilled cake piece into the warm raspberry mixture, using a fork to turn and coat all sides evenly. Allow the excess to drip off, then gently roll in the desiccated coconut, pressing lightly to adhere. Place each coated lamington on the wire rack.
12 - Let the lamingtons rest at room temperature for at least 30 minutes until the coating sets. Serve fresh with tea or coffee.