Heat oven to 375 degree F. Grease and flour two 9-inch round cake pans.
In a large bowl, whisk together flour, baking powder, and salt. Set aside.
In a clean bowl, beat the egg whites to soft peaks. Set aside.
In another large bowl, beat shortening and sugar until creamy. Add milk and flour mixture, alternating, in 3 additions, beating well after each addition. Beat in vanilla. Beat on medium-high speed for 5 minutes, occasionally scraping sides of the bowl. Gently fold in beaten egg whites.
Evenly divide between the pans. Bake at 375 degree F for 25 to 30 minutes or until a toothpick inserted in the center comes out clean. Cool on wire racks 10 minutes. Remove from pans and cool completely.
Whisk milk, flour, and salt in a medium-size bowl over simmering water or a double boiler, until very thick. Allow to cool. In another bowl, beat shortening, sugar, and vanilla until fluffy. Add cooled flour mixture; beat until fluffy.
Place one layer cake on serving plate and spoon 2 tablespoon cream of coconut on top. Let cake absorb. Frost top of layer and cover with some of the coconut. Top with second layer and spoon remaining cream of coconut over top. Frost top and sides; cover with remaining coconut. Chill at least 1 hour before serving. Makes 16 servings.