Step 1

Make the cake: Preheat the oven to 350˚. Butter three 8-inch round cake pans and line the bottoms with parchment, then butter the parchment. Dust with all-purpose flour and tap out the excess. Whisk the all-purpose flour, cake flour, baking powder and salt in a medium bowl. Set aside.

Step 2

Beat the butter and sugar in a large bowl with a mixer on medium speed until pale and fluffy, 3 to 5 minutes. Add the eggs and egg whites one at a time, beating well after each addition and scraping down the bowl as necessary. Beat in both extracts. Reduce the mixer speed to low and gradually beat in the flour mixture in three batches, alternating with the milk. Beat until just incorporated.

Step 3

Divide the batter evenly among the prepared pans. Bake until the cakes are golden around the edges and a toothpick inserted into the centers comes out clean, 40 to 45 minutes. Transfer to racks and let the cakes cool in the pans for 15 minutes. Remove the cakes from the pans, remove the parchment and return the cakes to the racks to cool completely.

Step 4

While the cakes cool, make the frosting: Combine the sugar and egg whites in a heatproof bowl set over a pan of simmering water (do not let the bowl touch the water). Whisk until warm and the sugar is dissolved, 3 to 4 minutes. Remove the bowl from the pan and beat with a mixer on medium speed until thick and glossy, 5 minutes. Increase the speed to medium high and beat until stiff peaks form and the bottom of the bowl is cool, 7 more minutes. Reduce the speed to medium low; Add the butter a few tablespoons at a time, beating well after each addition. (It’s OK if the frosting looks separated—just beat on medium-high speed until smooth again.) Add both extracts and the salt and continue beating until fluffy, 3 to 5 minutes.

Step 5

Trim the tops of the cakes with a long serrated knife to make them level, if necessary. Place 1 cake layer on a cake stand or platter. Spread with 1 cup frosting. Place the second layer on top and spread with another 1 cup frosting. Place the remaining cake layer on top and spread the remaining frosting over the top and sides of the cake. Press the coconut into the sides of the cake.