01 - Preheat the oven to 350°F. Line an 8-inch square baking pan with parchment paper, leaving a 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 mixing bowl, beat the softened butter and granulated sugar together using an electric mixer on medium-high speed until the mixture becomes pale, light, and fluffy, about 3 to 4 minutes.
04 - Add the eggs one at a time, beating well after each addition. Stir in the vanilla extract until fully incorporated.
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 combined, being careful not to overmix.
06 - Spread the batter evenly into the prepared baking pan using 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.
07 - Once completely cooled, remove the cake from the pan and trim any raised edges if necessary. Cut into 16 even squares. Place the squares on a tray and freeze for 30 minutes to firm up, which makes them easier to handle during dipping.
08 - In a wide bowl, whisk together the sifted powdered sugar and raspberry jam or puree. Add the milk one tablespoon at a time until the icing reaches a smooth, pourable consistency that coats the back of a spoon.
09 - Spread the desiccated coconut evenly in a shallow dish. Set a wire rack over a sheet of parchment paper to catch drips.
10 - Using two forks, dip each chilled cake square into the raspberry icing, turning to coat all sides. Allow the excess icing to drip back into the bowl, then immediately roll the coated square in the desiccated coconut, pressing gently to adhere. Place each finished lamington on the wire rack to set.