Cake
16 tablespoons (2 sticks) unsalted butter, softened
2 cups sugar
1 tablespoon pure vanilla extract
4 large eggs, separated, at room temperature
2 cups all-purpose flour
1 teaspoon baking powder
1 teaspoon baking soda
Pinch of salt
1 cup buttermilk, at room temperature
1 cup shredded sweetened coconut, toasted until golden
¼ teaspoon cream of tartar
Frosting
8 ounces cream cheese, softened
4 tablespoons (½ stick) unsalted butter, softened
1 pound powdered sugar
1 cup shredded sweetened coconut, toasted until golden
1. Preheat oven to 350˚F. Butter and lightly flour 3 9-inch cake pans.
2. Put the butter and sugar in a large bowl and cream together until fluffy, 4 to 5 minutes, using an electric mixer on medium speed. Add the vanilla and beat until smooth. Add the egg yolks, 1 at a time, beating for 20 seconds after each addition. Scrape down the bowl.
3. In a bowl, whisk together the flour, baking powder, baking soda, and salt. Add the flour mixture to the butter mixture in thirds, alternating with the buttermilk. Beat for 45 seconds after each addition and begin and end with the dry ingredients. Scrape down the bowl. Add the coconut and beat on low speed.
4. In a separate bowl, beat the egg whites until frothy using the electric mixer on high speed. Add the cream of tartar, and beat until stiff peaks form. Fold the beaten whites into the batter until no white streaks remain. Divide the batter evenly among the 3 prepared pans and smooth the top of each.
5. Bake on the middle rack of the oven for 25 to 30 minutes or until a toothpick inserted in the centers comes out clean. Remove the pans from the oven to wire racks to cool for 10 minutes. Invert the pans onto the racks and let cool to room temperature.
Make the frosting:
6. Put the cream cheese and butter in a large bowl and beat until smooth using the electric mixer on medium speed. Scrape down the bowl. Beat in the powdered sugar, a little at a time, until creamy and smooth. Scrape down the bowl. With a rubber spatula, gently fold in the toasted coconut and combine well.
Assemble the cake:
7. Place a cake layer on a serving plate with strips of wax paper under the edges and spread the top of it with frosting. Add the second layer and frost the top. Place the remaining layer on top. Frost the sides of the cake, then the top. Garnish by pressing the toasted coconut gently over the top and sides. If desired, place large flakes of coconut over the top. Remove the wax paper.