01 - Preheat the oven to 350°F (175°C). 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. Set aside.
03 - In a large mixing bowl, beat the softened butter and granulated sugar with an electric mixer on medium-high speed until 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 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 on a wire rack.
07 - Once completely cooled, lift the cake from the pan using the parchment overhang. Cut into 16 even squares. Place the squares on a tray and freeze for 30 minutes to firm up, which makes dipping much easier.
08 - In a shallow bowl, whisk together the sifted powdered sugar, raspberry jam or puree, and 2 tablespoons of milk. Add additional milk one teaspoon at a time until the glaze reaches a smooth, pourable consistency.
09 - Spread the desiccated coconut evenly in a shallow dish. Set up an assembly line with the icing bowl, coconut dish, and a wire rack placed over a sheet of parchment to catch drips.
10 - Working with one chilled cake square at a time, dip it into the raspberry icing, turning to coat all sides. Allow excess icing to drip off, then gently roll the square in the desiccated coconut, pressing lightly to adhere. Place each coated lamington on the wire rack to set for at least 15 minutes before serving.