Combine flour, sugar, baking powder, baking soda, and salt. Add milk, shortening, and vanilla. Beat with an electric mixer on low till combined, then for 2 more minutes on high. Add egg whites; beat 2 more minutes (on high). Don’t skimp on the beating–it whips air into the batter and makes a light cake! Pour into 2 greased round cake pans and bake at 350-degrees for about 25 minutes. Cool on wire racks.