Preheat the oven to 350°F. Prepare three 6-inch cake pans by spraying the sides with a cooking spray (Baker’s Joy is my favorite) and a wax paper circle fitted to the bottom of the pan. Alternatively, you can grease and lightly flour the pans.
Sift the cake flour and then measure by spooning and leveling it in your measuring cup. Add the cake flour, baking powder, baking soda, and salt into a bowl and whisk to combine. Set aside.
In the bowl of your stand mixer (a handheld mixer works fine too!), cream the butter on high for two minutes until it’s light and fluffy. Add the sugar and continue to mix on medium-high for another two minutes, scraping down the bowl and paddle as needed. Slowly add the egg whites while mixing on low until well combined. Add sour cream, vanilla extract, and coconut extract and mix for one minute on high, scraping down the bowl and paddle once more.
With the mixer on low speed, add in the dry ingredients and mix until just combined. Add the canned coconut milk slowly and mix until just incorporated. Gently fold in the shredded coconut by hand, making sure you scrape down the sides and bottom of the bowl without overmixing.
Pour batter evenly into prepared cake pans (no more than 2/3 full) and bake for 40-45 minutes. They’re done when they spring back to the touch and a toothpick inserted into the middle comes out clean. Let the cakes cool in the pan for five minutes before turning them out onto a wire rack for an additional few hours of cooling. Make sure they’re entirely room temperature before applying any frosting.