In a large bowl, whisk together the cake flour, baking powder, baking soda, and salt. Set this aside.
In a stand mixer fitted with a paddle attachment, beat the butter and sugar on medium-high speed for about 2 minutes, until it’s smooth and creamy.
Add in the egg whites and beat again until fully combined.
Now mix in the sour cream, vanilla extract, and coconut extract. Don’t worry if the mixture looks a little curdled—that’s totally normal when you combine these ingredients with butter.
With the mixer on low, gradually add the dry ingredients and coconut milk. Continue mixing until everything is just combined.
Fold in the shredded coconut by hand and make sure there’s no unmixed butter hiding at the bottom of the bowl. The batter will be thick!
Evenly divide the batter between the prepared pans and spread it out smoothly.
Place the pans on the center rack and bake for 20–25 minutes, or until a toothpick inserted in the center comes out clean.
Let the cakes cool in their pans on a wire rack.