01 - Preheat the oven to 350°F. Line an 8-inch square baking pan with parchment paper, leaving slight overhang on the sides for easy removal.
02 - In a medium bowl, whisk together the all-purpose flour, baking powder, and salt until evenly distributed. Set aside.
03 - In a large bowl using an electric mixer, beat the softened butter and granulated sugar on medium-high speed until the mixture turns pale, light, and fluffy, approximately 3 to 4 minutes.
04 - Add the eggs one at a time, beating well after each addition. Mix in the vanilla extract until fully combined.
05 - Gradually add the dry ingredient mixture to the wet ingredients in three additions, alternating with the whole milk in two additions. Mix on low speed just until each addition is incorporated, being careful not to overmix.
06 - Spread the batter evenly into the prepared baking pan, smoothing the top with a spatula. Bake for 22 to 25 minutes, or until a toothpick inserted into the center comes out clean. Allow the cake to cool completely in the pan on a wire rack.
07 - Once the cake is completely cool, lift it out of the pan using the parchment overhang. Cut into 16 even squares. Place the squares on a tray and freeze for 30 minutes to firm them up, which makes the dipping process much easier.
08 - In a shallow bowl, whisk together the sifted powdered sugar and raspberry jam or puree. Add the milk one tablespoon at a time until the glaze reaches a smooth, pourable consistency that coats the back of a spoon.
09 - Spread the desiccated coconut evenly in a shallow dish. Set up an assembly line with the chilled cake squares, the raspberry icing, and the coconut within easy reach.
10 - Using two forks, dip each chilled cake square into the raspberry icing, turning gently to coat all sides. Allow the excess icing to drip off, then transfer the square to the coconut. Roll and press gently to coat all surfaces evenly. Place each finished lamington on a wire rack and let them set for at least 15 minutes before serving.