Preheat the oven to 350°F (176°C). Line three 8-inch cake pans with parchment paper and grease the sides.

Beat the butter and sugar in a large bowl on medium speed about 2 minutes until light and fluffy. Scrape down the sides of the bowl.

Add egg whites and vanilla and beat on medium speed for about 1 minute until the mixture thickens and may look slightly curdled.

Combine flour, baking soda, and baking powder in a medium bowl.

Add about one-third of the dry ingredients to the batter and beat until incorporated.

Add half of the milk and beat until combined.

Alternate adding the dry and wet ingredients until all are incorporated, ending with dry ingredients. The batter should be thick and glossy.

Divide the batter evenly among the prepared cake pans and spread evenly.

Bake for 30-33 minutes or until a toothpick inserted in the center comes out clean. Let cakes cool for 5 minutes before removing from pans.

Remove cakes from pans and cool completely on wire racks.

In a mixing bowl, beat the shortening and butter until smooth. Gradually add powdered sugar and beat until smooth. Mix in vanilla and water or milk until desired consistency is reached.

Assemble the cake by placing the first layer on a serving plate, spreading icing, then layering the second cake, and adding icing again. Top with the final cake layer and cover the outside with remaining icing.