Stir together flour, salt and baking powder in a bowl. In the bowl of an electric mixer, beat shortening on high until softened. Gradually add sugar and vanilla, mixing on a low speed for a short period in between. Add egg yolks one at a time, beating shortly after each addition on a low speed. Add alternately by fourths, flour mixture then milk, beating shortly on a low speed after each addition. This is a lot of mixing, and you don't want to over-mix the batter, or the texture won't be right, so you don't need to completely mix in the ingredients (just mostly) in between each mix session. In the end you will want things to be completely incorporated, but don't worry about it as much in between.

Beat egg whites in a separate bowl until stiff peaks form. Fold into batter, no more than 30 strokes (you don't want to over-mix or it could turn out too heavy and dense). Do just enough strokes to mostly incorporate the egg whites, but it's ok if a little is still showing through in the batter. Bake at 375 degrees Fahrenheit in three greased and floured 9 inch layer pans or two 9 inch square pans. If doing three layers, bake for approximately 20 minutes, or just until a toothpick inserted into the center comes out clean.

Let cool in pans for about 5 minutes, then carefully remove to a cooling rack to cool completely.

For the frosting, cream together all ingredients in the bowl of an electric mixer until very creamy and easily spreadable, but not too thin. I like to add a tablespoon of milk at a time and mix in between, until desired consistency is reached.

Frost cooled cakes.