Preheat the oven to 350°F. Line the bottom of 3, 8-inch round cake pans with parchment paper and spray with nonstick cooking spray. Set aside.
In a large bowl, whisk together the cake flour, baking powder, and salt. Set aside.
In the bowl of a stand mixer with the paddle attachment, cream together sugar, butter, vanilla extract, and almond extract on medium speed until light and fluffy, about 5 minutes, stopping to scrape the bowl as needed.
With the mixer on low, add egg whites, one at a time, beating well after each addition, stopping to scrape the bowl as needed.
Add ⅓ of the flour mixture, half of the milk, another third of the flour mixture, the remaining milk, and then the remaining flour mixture. Mix just until combined, stopping to scrape the bowl as needed.
Distribute the batter evenly into the three prepared pans. Bake for 22-24 minutes, or until a toothpick inserted in the center comes out clean. Allow the cakes to cool completely on a wire rack.