01 - Preheat the oven to 350°F. Line an 8-inch square baking pan with parchment paper, leaving slight overhang on the edges for easy removal.
02 - In a medium bowl, whisk together the all-purpose flour, baking powder, and salt until evenly distributed.
03 - In a separate large bowl, beat the softened butter and granulated sugar with an electric mixer on medium speed until pale, light, and fluffy, about 3 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. Fold gently after each addition, mixing only until just combined to avoid overworking the batter.
06 - Pour the batter into the prepared pan and spread evenly 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 completely cooled, lift the cake from the pan using the parchment overhang. Using a serrated knife, trim the edges and cut the cake into 16 even squares. Place the squares on a tray and freeze for 30 minutes to firm up for easier handling during dipping.
08 - In a shallow bowl, whisk together the sifted powdered sugar and raspberry jam or puree. Add whole milk one tablespoon at a time, stirring 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 large enough to accommodate rolling the cake squares.
10 - Working one at a time, dip a chilled cake square into the raspberry icing, using two forks to turn and coat all sides evenly. Allow excess icing to drip off briefly, then transfer the square to the coconut dish. Roll gently to coat all surfaces. Place each finished lamington on a wire rack and allow the icing to set completely before serving.