Cream the butter and sugar in a stand mixer until light a fluffy, about 5 minutes on high speed.
While that is creaming, combine the egg whites, milk, and vanilla in a medium bowl and set aside.
In another bowl, sift together the all-purpose and cake flours, baking powder, and salt.
With the mixer on low, add in about ⅓ of the sifted dry ingredients to the creamed butter mixture.
Next add egg white mixture slowly while continuing to mix on low speed. (you may need to scrape the sides of the bowl)
Repeat the same pattern; add your dry ingredients and then the remaining liquid. Add in the remaining flours.
Pour immediately into 9x13 baking pan that has been prepared with pan release.
Bake in preheated 350° F oven for approximately 25-30 minutes or a toothpick inserted is removed mostly clean.
Allow cake to cool completely.