
1 1/2 cups milk, at room temperature
1 1/4 cups egg whites (about 9 eggs), at room temperature
1 tablespoon vanilla
3 1/4 cups plus 2 heaping tablespoons cake flour
2 cups granulated sugar
2 tablespoons baking powder
1 1/2 teaspoons salt
1 cup plus 2 tablespoons unsalted butter, at room temperature (2 1/4 sticks)
Preheat oven to 350 degrees. Grease and flour two 9-inch cake pans. Line the bottom of each pan with wax or parchment paper. Grease and flour the top side of the paper.
Into a medium bowl, blend together the milk, egg whites and vanilla with a fork. In the bowl of a stand mixer, add the cake flour, sugar, baking powder and salt. Mix on low until just combined. Add the butter; mix on low until coarse and crumbly, about 3 minutes. Add all but 3/4 cup milk mixture to the flour mixture; mix on medium for 11/2 minutes. Add remaining 3/4 cup milk mixture and beat for 30 additional seconds. Stop mixer to scrape down sides and bottom of the bowl, then continue mixing for 20 more seconds.
Divide the batter between the prepared pans, using a spatula to evenly spread the batter. Bake in the center of the oven, making sure the pans are 3 inches apart and do not touch the oven sides. Bake until the cakes are springy to the touch and a toothpick inserted in the center comes out clean, about 30 minutes. Let the layers cool in their pans for 15 minutes. Gently loosen the edges with a thin knife before inverting the layers onto wire racks. Let the cakes cool thoroughly before carefully peeling off the paper. Cool completely before frosting.
Frosting
5 egg whites
11/2 teaspoons vanilla
1/4 teaspoon cream of tartar
Pinch of salt
13/4 cups granulated sugar
1 cup water
3 cups sweetened flaked coconut
In a clean bowl of stand mixer, beat the egg whites on low for 1 minute. Add vanilla, cream of tartar and salt. Beat on medium to form soft peaks. Increase to high and beat to stiff peaks. Meanwhile, combine the sugar and 1 cup water in a small saucepan. Bring to boil, cover and boil for 2 minutes. Uncover pan and continue to boil until candy thermometer reaches 238 degrees. Return the mixer to high, add the sugar syrup in a thin stream and continue to beat, scraping down the sides of the bowl as necessary, 7 to 10 minutes. Use frosting immediately.
To assemble cake
Place a dollop of frosting in the middle of the serving platter.
Place the bottom layer of the cake on the platter, top side down. Using a narrow metal spatula, spread one-third of the frosting over the bottom layer. Place the remaining layer on top. Spread the rest of the frosting over the top and sides of the cake. Generously sprinkle the top and sides with the coconut, pressing the coconut into the sides.