Coconut-Cream Cake

To prepare the filling, mix 3 tablespoons of the coconut milk with the cornstarch. Set aside.

In a medium-sized saucepan, bring the remaining coconut milk, half-and half, 1/4 cup sugar, and salt to a simmer over medium-high heat, stirring for 2 minutes or until sugar is dissolved.
Whisk together 4 egg yolks, 1/4 cup sugar, and 1/2 teaspoon vanilla in a medium bowl; slowly pour in the coconut-milk mixture, whisking continously.

Return the liquid to the saucepan; whisk continuously while the cream simmers over low heat until it begins to thicken, about 5 minutes.

Whisk in the cornstarch mixture, cook for 2 minutes, and add 1 tablespoon butter. Stir until melted. Remove from the heat and blend in 1/2 cup toasted coconut.

Transfer to a bowl and lay a piece of platic wrap on top of the cream filling to prevent a skin from accumulating on the surface. Refrigerate for at least 2 hours, or until set.

Preheat the oven to 350 degrees. Butter and flour three 10-inch cake pans.

For the cake, sift the flour, baking powder, baking soda, and salt together and set aside.

In the bowl of an electric mixer, beat 1 pound butter on medium speed for 1 minute. Add 2 1/2 cups sugar, and 7 egg yolks one at a time, beating after each addition. Add 1 tablespoon vanilla and beat until mixture is fluffy, about 3 minutes. Lower the speed and mix in half the dry ingredients. Add the milk, then the remaining dry ingredients.

In a separate bowl, whip the 7 egg whites with the cream of tartar until soft peaks form. Fold some of the whites into the cake batter to loosen up the batter and prevent the whites from breaking down. Add the remaining whites, folding in gently until incorported. Divide batter among the three prepared pans and bake for 20 minutes, or until a skewer inserted into the cake comes out clean. Cool.

To assemble the cake, place one layer on a plate and spread with half of the coconut-cream filling. Place the second layer on top the filling and spread with the remaining filling. Place the third layer on top.

To make the frosting, beat together 4 ounces butter and cream cheese in the bowl of an electric mixer until smooth. On low speed, add the confectioners' sugar, heavy whipping cream , 2 teaspoons vanilla, and salt and beat for 1 minute. Increase the speed to high and beat until fluffy, about 2 minutes. Immediately spead the frosting in a thin layer on the top and sides of the cake. Press the toasted coconut all over into the frosting.