Southern Coconut Layer Cake With Divinity Icing

For the cake:

1. Preheat the oven to 350 degrees F. Butter and flour two 9-inch round cake pans; set aside. Sift the flour, baking powder and salt onto a sheet of wax paper; set aside.
2. With an electric mixer at medium-high speed, cream the butter and sugar until very light and smooth. Add all of the egg whites and the vanilla and almond extracts; beat until well combined and smooth. Add ½ cup of the milk and mix well. Lower the speed to slow and add the sifted ingredients; mix just until blended, no longer. Fold in the remaining ½ cup milk. Divide the batter between the prepared pans; smooth the top.
3. Bake until the cake layers are golden brown, the edges shrink slightly away from the sides of the pans, and a toothpick inserted in the centers emerges clean, 40 to 45 minutes.
4. Cool the cake layers in their pans on a wire rack for 10 to 15 minutes. Run the tip of a knife around the sides of the cakes to loosen them; invert the cakes, turn right side up and cool to room temperature.

For the divinity icing:

1. Combine the sugar, corn syrup and cold water in a small, heavy saucepan. Bring to a boil over medium heat, stirring to dissolve the sugar. Boil, uncovered, until the syrup reaches a temperature of 240 degrees F, usually 3 or 4 minutes. (This is the soft-ball stage. If you don’t own a candy thermometer, drop a small spoonful of the hot syrup into a cup of ice water; the mixture will form a soft mass when pressed between your fingers.)
2. While the syrup is cooking, beat the egg whites, cream of tartar and salt with an electric mixer at medium-high speed until foamy. When the syrup reaches the soft-ball stage, slowly pour it into the beaten whites in a very slow, thin stream, beating all the time. (Try to pour the syrup into the center of the egg whites, so it doesn’t spatter all over the sides of the bowl.) When all of the syrup has been added, add the vanilla and continue to beat until the mixture is fluffy and shiny and cools to room temperature, usually 7 to 8 minutes. Beat in the lemon juice and hot water.
3. With a long serrated knife, split each cooled cake layer horizontally into 2 layers. Sprinkle the cut side of each layer with 1 tablespoon of the coconut milk or thinned coconut cream.
4. Choose a layer with a flat surface and set it aside for the top. Place 1 of the layers, cut side up, on a serving plate. Spread it with a generous layer of icing; sprinkle on some coconut. Repeat with the remaining layers, spreading each with icing and coconut. Gently press the reserved layer, browned side up, on top.
5. Spread the top and sides of the cake with the remaining icing. Sprinkle the top of the cake with coconut, and gently press more coconut into the icing on the sides.