Coconut Layer Cake

Directions

1. 1
   For the cake: Preheat oven to 350° F. Butter four 8-inch or 9-inch cake pans. Line the pans with parchment rounds, then butter and flour the pans and paper.
2. 2
   In a stand mixer, combine the 10 whole eggs, 1 1/2 cups sugar, and 1 tablespoon vanilla extract. Beat on high until the mixture nearly triples in volume, 7 to 10 minutes. Note: This filled the bowl of my kitchen aid mixer, nearly to the top.
3. 3
   With the mixer on, slowly stream in the oil until well mixed. In a medium bowl, whisk the flour and salt together.
4. 4
   Gently fold the flour mixture into the egg mixture until well mixed. (You may need to transfer the egg mixture to a large mixing bowl to do this, and it's always best to use a big, wide bowl when folding ingredients together to lower your chances of deflating the batter too much.)
5. 5
   Divide the batter between the pans and tap them lightly on the counter to remove any large bubbles. Bake the cakes until they are golden and a toothpick inserted into the center comes out clean, 20 to 25 minutes. Let the cakes cool in their pans, on a rack, until cool to the touch, then turn them out onto the rack, and remove the parchment. Let cool completely.
6. 6
   For the syrup: Combine the water and 1/3 cup sugar in a small saucepan over medium heat. Cook until the sugar dissolves then stir in the rum and shredded coconut. Let the mixture cool completely before using.
7. 7
   For the buttercream: Combine the egg whites and 1 1/4 cups sugar in a glass or stainless steel bowl set over a pan of simmering water. Whisk the mixture constantly until the sugar dissolves and is hot to the touch. Remove from the heat and whip on high speed until light and fluffy and the meringue has cooled to room temperature.
8. 8
   Turn the mixer down to medium and add the butter, one tablespoon at a time, until all of the butter is incorporated. If the buttercream curdles at any point, turn the mixer up to high and whip until it emulsifies. Add the extracts and a pinch of salt.
9. 9
   To assemble: Place one cake layer on a serving plate or pedestal. Brush with the syrup and scatter 1/3 of the syrup-moistened coconut over the top. Spread with about 1 cup of frosting, repeat with two more cake layers, then top with the final layer. Spread the remaining frosting over the cake, smooth the top and press the toasted coconut flakes into the sides.