Preheat oven to 350º F. Spray 2 9-inches pans with the baking spray. Set aside.
In a large bowl, sift together the flour, baking powder, and salt. Set aside.
Beat the butter with an electric mixer on high speed until creamy; 5 minutes. Add 2 cups of the sugar and continue beating, scraping down the sides of the bowl, until light and fluffy; 5 more minutes. Reduce speed to low. Add the flour mixture into the butter, one cup at the time, alternating with the milk, until smooth. Add 1 teaspoon of the vanilla and the coconut extract and mix until incorporated.
In a large bowl beat 8 of the egg whites with an electric mixer to stiff peaks. Fold 1/2 cup whites into the batter until blended, then fold in the remaining whites.
Divide the batter in 2 and pour into the previously prepared pans. Bake in the oven for 30 – 35 minutes or until a skewer inserted in the center comes out clean.
Make the frosting by combining the remaining 2 egg whites, the remaining 1 1/2 cups sugar, the water, cream of tartar and corn syrup in a heatproof bowl of a stand mixer. Place the bowl over simmering water, stirring the mixture until all the sugar has dissolved and looks thick and shiny. Remove from heat; add the remaining 1 teaspoon of vanilla extract. Move the bowl to the stand mixer fitted with the wire attachment. Beat the egg whites to a stiff peak on high speed, until the egg whites have cooled to room temperature.
In a small bowl, combine 1 cup icing and 1 cup of the coconut; stir to mix. Set aside.
If your cakes are not even you can cut them with a wire cake cutter. Just set your cake on a flat and level surface. Hold the cake cutter by the handle and pull it evenly through the cake. The cake has to be completely cool to do this or it may crumble.
Place the first cake on the platter or cake stand to frost. Add the frosting you mixed with coconut on top and spread evenly. Set the 2nd cake on top, spread the plain icing evenly working your way down the sides until you have a thin layer of frosting over the entire cake.
Pat the toasted coconut evenly onto the sides and top.