Prepare Buttercream: Beat butter in a medium bowl at medium speed with an electric mixer until creamy. Gradually add powdered sugar, beating at low speed until blended after each addition. Gradually add milk and next 3 ingredients, beating at low speed until blended. Increase speed to medium, and beat 1 to 2 minutes or until smooth.
Place 1 Basic White Cake layer on a serving platter. Spread half of buttercream over cake layer. Top with second layer, and spread remaining buttercream over cake layer. Top with third cake layer.
Prepare Frosting: Pour water to a depth of 1 1/2 inches into bottom of a double boiler over medium heat; bring to a boil. Stir together egg whites, next 3 ingredients, and 1/2 cup water in top of double boiler; beat at low speed with a handheld electric mixer until blended. Place top of double boiler over boiling water, and increase mixer speed to high. Beat 7 minutes or until soft glossy peaks form and frosting is spreading consistency. Remove from heat, and stir in vanilla. Spread immediately over top and sides of cake.