Coconut Cake

Ingredients:
Filling:
1 ¼ cups heavy cream
¾ cup granulated sugar
2 T coconut cream
1 T cornstarch
1 T milk
½ cup unsalted butter, softened
1 cup shredded coconut

Cake:
3 cups all-purpose flour
1 T baking powder
¼ tsp salt
1 ½ cups granulated sugar
4 eggs
¾ cup unsalted butter, cut into small pieces, softened
1 T vanilla extract
1 cup milk

Frosting:
6 ounces cream cheese, softened
½ cup unsalted butter, softened
¼ tsp salt
1 lb. confectioners sugar
3 T milk
1 T vanilla extract

Syrup and Garnish:
1 cup granulated sugar
1 cup water
¼ tsp vanilla extract
½ cup shredded coconut. (Frozen coconut is great if you can find it where you live. We think it might be a "Southern coastal" thing, since we've never been able to find it in Denver. If they sell frozen coconut where you live, go for it.)
Prepare the filling:Place the heavy cream, sugar, and coconut cream in a heavy saucepan over medium heat and bring to a simmer. Stir the cornstarch and the milk together in a small bowl until there are no lumps. Whisk the cornstarch mixture into the simmering cream until it's smooth; cook, stirring, for 3 minutes longer. Add the butter and shredded coconut and continue cooking, stirring, for 3 more minutes. Cool to room temperature and then refrigerate until thickened, about 2 hours.
Preheat the oven to 350 degrees F.
Grease three 9-inch round cake pans and line the bottoms with waxed paper. Grease the paper and then flour the pans lightly, tapping out any excess.
Prepare the cake:Sift the flour, baking powder, and salt together. Reserve. Place the sugar and eggs in a large mixing bowl and beat with an electric mixer for 1 minute. Gradually add the butter, vanilla, and milk and continue beating for 2 minutes. Add the reserved dry ingredients and beat for 1 minute.
Scrape the batter evenly into the prepared pans and bake for 20 minutes or until a wooden pick inserted into the center comes out clean.
Cool the cakes in the pans on a rack for 20 minutes. Un-mold the cakes, carefully peeling off the waxed paper and allow them to cool completely on the rack.
Prepare the icing:Place the cream cheese and the butter in a bowl and beat with a mixer until creamy. Add the remaining icing ingredients; beat until smooth and soft.
Prepare the syrup:Place the sugar, water and vanilla in a small saucepan and bring to a boil. Boil for 3 minutes, stirring occasionally Remove from heat and brush the top of each cake layer with the syrup using a pastry brush. (You don't have to use all the syrup).
Assemble the cake:Place one cake layer on a serving platter. Spread it with half of the reserved filling and top with another layer of cake. Spread the cake with the remaining filling and top with the last cake layer. Ice the top and sides of the cake with the icing and then sprinkle the top with ½ cup shredded coconut.