Preheat your oven to 350°F (175°C). Grease two 8-inch round cake pans, line the bottoms with parchment paper, and dust the sides with a little flour. Proper pan preparation ensures your delicate cakes release without tearing.
In a medium bowl, whisk together the room temperature egg whites, whole milk, sour cream, clear vanilla extract, and almond extract until perfectly smooth. Set this mixture aside.
In the bowl of a stand mixer fitted with the paddle attachment, combine the cake flour, granulated sugar, baking powder, and salt. Mix on low speed for 30 seconds just to distribute the leavening agents evenly.
With the mixer on low, add the cubed, room-temperature butter one piece at a time. Continue mixing until the mixture resembles coarse sand. Coating the flour with fat before adding liquids is the secret to limiting gluten development.
Add half of the egg white mixture to the dry ingredients. Beat on medium speed for exactly 1 minute to build structure. Scrape down the sides. Add the remaining liquid mixture and beat for another 30 seconds until just combined.
Divide the batter evenly between the prepared pans. Bake for 30-35 minutes, or until a toothpick inserted into the center comes out clean. Let cool in pans for 10 minutes before turning out onto a wire rack.