Preheat oven to 350 degrees F. Butter and lightly flour three 6-inch cake pans. Line bottom with parchment paper and set aside.
Sift together cake flour, baking powder, salt, cinnamon, turmeric, and black pepper. Set aside. In another bowl, whisk together fresh ginger, milk, egg whites, and vanilla until smooth. Set aside.
In the bowl of a stand mixer fitted with a paddle attachment, beat butter and sugar until smooth. Scrape down bowl as needed to ensure thorough mixing.
Add 1/3 of dry flour mixture. Mix on slow speed while adding 1/2 of liquid mixture. Adding another 1/3 of dry mixture, follow with remaining liquid mixture, end with remaining dry mixture. Mix until batter is well combine. Scrape down bowl as needed.
Divide batter evenly among prepared cake pans. Bake for 30-35 minutes until toothpick inserted in center of cake comes out clean. Let cake cool in pan for 5 minutes before unmolding. Allow cake layers to cool to room temperature on wire racks.
If necessary, use a serrated knife to level off cake layers once cake has completely cooled.