Lemon-Coconut Cake

Combine sugar and cornstarch in a medium saucepan; whisk in 1 cup boiling water. Cook over medium, whisking constantly, until sugar and cornstarch dissolve, about 2 minutes. Beat egg yolks in a medium bowl. Gradually whisk about 1/4 of hot sugar mixture into egg yolks; add to remaining hot sugar mixture in pan, whisking constantly. Whisk in lemon zest and juice.

Cook, whisking constantly, until mixture is significantly thickened, 3 to 5 minutes. Remove from heat. Whisk in butter; cool completely, at least 1 hour, stirring occasionally.

Preheat oven to 350°F. Butter and flour 3 (9-inch) round cake pans.

Beat butter in a large bowl with an electric mixer at medium speed until creamy, about 1 minute. Gradually add sugar, beating until light and fluffy, about 3 minutes. Add egg yolks, 1 at a time, beating until blended after each addition and scraping down sides of bowl if needed.

Whisk together flour, baking powder, and salt in a bowl; add to butter mixture alternately with milk, beginning and ending with flour mixture. Beat at low speed until blended after each addition. Stir in vanilla.

In a medium bowl, beat egg whites at high speed with electric mixer until stiff peaks form; about 6 minutes. Fold ⅓ of egg whites into batter. Gently fold in remaining beaten egg whites just until blended. Spoon batter evenly into prepared cake pans. Bake in preheated oven until a wooden pick inserted in center comes out clean, 22 to 28 minutes. Cool in pans on wire racks 10 minutes; remove from pans, and cool completely on wire racks, at least 1 hour.

Beat cream cheese and butter at medium speed with an electric mixer until creamy, about 1 minute. Gradually add powdered sugar, beating at low speed until blended, about 3 minutes; stir in vanilla.

Place 1 cake layer on desired serving platter or cake stand. Spoon 1/2 cup Cream Cheese Frosting into a piping bag fitted with a 1/2-inch round tip (or a plastic bag with bottom corner cut off). Pipe a 1/2-inch ring of frosting around outer edge of cake layer. Spoon 1 cup Lemon Filling inside frosting ring, and spread evenly. Top with second cake layer, and repeat procedure with frosting ring and remaining 1 cup Lemon Filling. Place third cake layer on top; spread remaining Cream Cheese Frosting on top and sides of cake. Sprinkle sides of cake with coconut. Garnish with lemon wedges, if desired.