Preheat oven to 325 degrees F (150 C Degrees). Grease three 8-inch round cake pans.
In a medium bowl whisk together the gluten-free flour, baking powder, and salt.
In the bowl of a stand mixer, cream together butter, shortening, and sugar until very light and fluffy, about 5 minutes. Add the egg whites, one at a time. Allow each egg white to incorporate before adding the next. After adding the last egg white, add the vanilla extract. Mix the batter for about 50 seconds. It should appear very light and fluffy--almost like frosting.
Reduce speed to low. Add about 1/3 of the flour, followed by the sour cream. Then, alternate between the remaining flour and milk, allowing each to almost incorporate before adding the next. After the last addition of milk, mix the batter until smooth, about 50 seconds.
Divide the batter evenly among the cake pans. Smooth the batter evenly into each pan with the back of a spoon.
Bake the cakes for about 25min or until a toothpick inserted into the middle comes out with only a few crumbs attached.
Allow cakes to cool in the pan for 10 minutes and turn out onto a wire rack to cool completely before frosting.