1 In a small bowl, sift 2 1/2 cups flour, baking powder, and salt together and set aside.
2 Blend shortening and 1 1/2 cups sugar. Mix in the flour mixture. Add 3/4 cup milk; beat for 2 minutes. Add egg whites, 1 teaspoon vanilla and 1/4 cup milk. Beat well.
3 Grease and flour two 9 inch round pans. Pour the batter into the pans.
4 Bake at 350 degrees F (175 degrees C) for 30 to 35 minutes. Cool cake layers on a wire rack.
5 Remove the meat from the coconut and shred it.
6 To Make Frosting: Moisten 1 tablespoon flour with a small amount of water to make a paste. Combine 1 cup milk, coconut milk, 1 cup sugar, 1 teaspoon vanilla, and shredded coconut in a saucepan. Mix in flour paste, and cook for 10 minutes. Cool the frosting, and spread over cake.