Allow egg whites to stand at room temperature for 30 minutes. Meanwhile, grease and lightly flour two round cake pans of one 13 x 9 rectangular cake pans and set aside. Preheat the oven to 350 degrees.
In a medium bowl, stir together flour, baking powder, baking soda and salt; set aside. In a large mixing bowl, beat shortening on medium to high speed for 30 seconds. Add sugar and vanilla; beat until well combined. Add egg whites one 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. Spread batter into the prepared pans.