Note: Room temperature ingredients make all the difference in this cake.
2 cups all purpose flour
1-1/3 cups sweetened, flake coconut
1 cup buttermilk
1 teaspoon baking soda
2 cups sugar
1 cup (2 sticks) unsalted butter, at room temperature
5 duck egg yolks
5 duck egg whites, at room temperature
3 cups powdered sugar
1 package of cream cheese, room temperature
1/2 cup (1 stick) butter, room temperature
2 teaspoons vanilla
1 cup flaked coconut
Preheat oven to 350°F. Coat two 9-inch-diameter cake pans with 1 1/2-inch-high sides with nonstick spray; line bottom of pans with parchment paper rounds.
Mix flour and coconut in medium bowl. Whisk buttermilk and baking soda in small bowl. Using electric mixer, beat sugar and butter in large bowl until light and fluffy, about 2 minutes. Add egg yolks and beat to blend. Add flour mixture in 3 additions alternately with buttermilk mixture in 2 additions, beating just to blend after each addition. Using clean dry beaters, beat egg whites and 1/4 teaspoon salt in another large bowl until peaks form. Add 1/3 of egg white mixture to batter; fold into batter just to blend. Fold in remaining egg white mixture in 2 additions. Divide batter between pans.
Bake cakes until tester inserted into center comes out clean, about 35 minutes. Cool cakes in pans on racks 10 minutes. Run small sharp knife around sides of cake pans. Invert cakes onto racks. Carefully peel off parchment. Cool cakes completely.
Using electric mixer, beat sugar, cream cheese, butter, and vanilla in large bowl until blended. Place 1 cake layer, flat side up, on plate. Spread with 1 cup frosting. Place second layer, flat side up, atop frosting. Spread remaining frosting over top and sides of cake. Sprinkle some of coconut over top of cake; pat more coconut on sides of cake.
DO AHEAD: can be made 1 day ahead. Cover and refrigerate. Let stand at room temperature 1 hour before serving.