Preheat oven to 350ºF. Line cupcake pans with paper liners.
Combine flour, sugar, baking powder, salt, shortening, milk and vanilla in a large mixing bowl. Mix at low speed for 2 minutes. Scrape bowl. Add egg whites and additional whites or yolks, and mix at high speed until fluffy and smooth, approximately 2 minutes.
Fill liners 1/2 to 2/3 full of batter. Do not overfill. Bake 20-25 minutes or until toothpick inserted in center comes out clean. Let cool 10 minutes in pans then remove from pan, and place on wire racks to cool completely.
In a piping bag, wipe the blue frosting against the side of 1/3 of the inside of the bag. Next wipe the green next to it, spreading it in the same fashion. Fill in the rest of the bag with the yellow frosting.