Grease and lightly flour two 8x11/2-inch round cake pans or grease one 13x9x2-inch baking pan; set the pan(s) aside. In a medium bowl stir together the flour, baking soda, and salt; set aside.
In a large mixing bowl beat shortening with an electric mixer on medium to high speed for 30 seconds. Add brown sugar and vanilla; beat until well combined. Add egg yolks 1 at a time, beating well after each addition. Alternately add flour mixture and buttermilk to shortening mixture, beating on low speed after each addition just until combined.
Thoroughly wash the beaters. In a medium mixing bowl beat egg whites with an electric mixer on medium speed until stiff peaks form (tips stand straight). Gently fold egg whites into the beaten mixture. Spread batter into the prepared pan(s).
Bake in a 350 degree F oven for 30 to 35 minutes for the 8-inch pans or 35 to 40 minutes for the 13x9x2-inch pan, or until a wooden toothpick inserted near centers comes out clean. Cool cake layers in pans on wire racks for 10 minutes. Remove cake layers from pans; cool thoroughly on racks. Or, place 13x9x2-inch cake in pan on a wire rack; cool thoroughly. Frost with Delicious Icing. Cover and store cake in the refrigerator for up to 3 days. Let stand at room temperature for 30 minutes before serving. Makes 12 to 16 servings.
In a screw-top jar combine milk and flour. Cover and shake well. Place milk mixture in a small saucepan. Cook and stir over medium heat until thickened and bubbly. Reduce heat; cook and stir for 2 minutes more. Remove from heat. Transfer cooked mixture to a small bowl. Cover surface with plastic wrap and refrigerate at least 2 hours or until thoroughly chilled. In a large mixing bowl beat butter, sugar, and vanilla with an electric mixer on medium speed until light and fluffy and sugar is almost dissolved. Add the chilled cooked mixture, 1/4 at a time, beating on medium speed after each addition until smooth. Makes about 3 1/4 cups icing.