Preheat oven to 350° F. Sift together flour, baking powder and salt.; In a separate bowl, cream shortening and sugar together until light and fluffy. Combine milk and vanilla extracts; add alternately with dry ingredients. Stir just until smooth after each addition. Fold in egg whites.
For a 2-layer cake: Pour batter into 2 8-inch rounds and bake for 25-30 minutes.
For cupcakes: Pour batter into muffin tin and bake for 20-25 minutes.
While the cakes/cupcakes cool, prepare the frosting. Beat the butter until smooth and fluffy, it should visibly lighten in color. Add the powdered sugar, 1/2 cup at a time, and beat until incorporated. Add 2 tablespoons of the heavy cream and beat well on medium speed. Add the vanilla extract. If the mixture is too stiff, add more milk until the mixture is firm and creamy.
Pipe frosting onto cake/cupcakes once they are completely cooled.
Recipe from the Rumford Complete Cookbook, 1950 edition.