This is one of King Arthur Baking's older white cake recipes. The mixing technique is unusual! You cream the butter, sugar, baking powder, salt and extracts until very light. You then add the egg whites, one by one, followed by the cake flour and milk.
Preheat oven to 350 degrees F. Grease and flour pans of choice. You can use 8-inch round, 9-inch round or a 9x13 inch pan.
With an electric mixer, cream together butter, shortening, sugar, baking powder, salt and extracts until light and fluffy (about 5 minutes, maybe longer if butter is cool).
Add egg whites one at a time and beat well after each addition.
Stir in flour and milk, alternating between the two, starting and ending with the flour. (i.e. ⅓ flour, ½ milk, ⅓ flour, ½ milk, ⅓ flour)
Pour into pans (2 9-in. round or one 9x13-in) and bake at 350. 25-30 minutes or until done.
Notes
Update: King Arthur has updated the recipe a bit and it is now called Tender White Cake. For a slightly revised version that uses all butter and a different mixing technique, check out King Arthur's site.