To make the cake, heat the oven to 325°F with a rack in the middle position. Mist the interior of an 8-inch square baking pan with cooking spray, dust with flour, then tap out the excess. Line with Kitchen parchment. In a 2-cup liquid measuring cup or small bowl, whisk together the egg whites, the milk and vanilla; set aside.

In a stand mixer fitted with the paddle attachment, combine the flour, sugar, baking powder and salt, then mix on low until combined, about 10 seconds. With the mixer running, add the butter one piece at a time.

Once all the butter has been added, continue mixing until sandy and no large butter pieces remain, 2 to 3 minutes. With the mixer still running, pour in all but ¼ cup of the egg-milk mixture and mix until combined.

Increase to medium-high and beat until light and fluffy, about 1 minute. Reduce to medium, then slowly add the remaining egg mixture, scraping the bowl once or twice.

Transfer the batter to the prepared pan and spread evenly. Bake until light golden brown and a toothpick inserted at the center comes out clean, 30 to 35 minutes. Cool in the pan on a wire rack for 10 minutes, then run a paring knife around the edges to loosen.

Invert the cake onto a large plate, lift off the pan and remove and discard the parchment. Re-invert the cake onto the rack to be right side up and cool completely, about 2 hours.

Line a rimmed baking sheet with kitchen parchment. Using a serrated knife, trim off the edges of the cake, then cut the cake into 16 even squares. Place the squares on the prepared baking sheet, cover with plastic wrap and freeze until firm, at least 1 hour or up to 2 days.

To make the glaze in a medium saucepan over high, bring 1 inch of water to a boil, then reduce to medium-low. In a medium heat-proof bowl that fits on top of the saucepan, combine the milk, chocolate and coconut oil.

Set the bowl on the saucepan, over the simmering water, and warm the mixture, whisking gently and occasionally, until melted and smooth. Remove the bowl from the pan, then whisk in the powdered sugar and salt; reserve the saucepan and warm water. Place the coconut in a small bowl.