Preheat your oven to 350 degrees. Then, grease your three 9-inch cake pans. And line them with parchment paper. After that, grease the parchment paper as well. Remember, the parchment paper will help you release the cake from the cake pans easily.
Afterward, prepare a large mixing bowl. And whisk your cake flour, baking powder, baking soda, and salt together using a whisk. Then, set it aside.
In a different mixing bowl, beat your butter and sugar. With that, make sure to utilize an electric mixer attached with a whisk or paddle attachment. After that, beat the mixture at medium-high speed for about two minutes. Or do it until the mixture becomes smooth and creamy.
Next, scrape your bowl's sides and bottom using a rubber spatula. Doing this incorporates everything. Then, put the egg whites into the mixture. And beat it until it combines well. Afterward, add the sour cream, vanilla extract, and coconut extract. Make sure to beat until well-combined. Note that the batter may look curdled due to the various textures. Likewise, solid butter combined but, do not worry. After that, scrape the bowl's sides and bottom as needed.
Then, set your electric mixer at low speed. Afterward, gradually add your dry ingredients and coconut milk. Ensure to beat at a low speed until everything combines well. And add the shredded coconut. After that, whisk by hand to ensure no butter lumps at the bottom of your bowl. Do that till your cake batter becomes slightly thick.
Afterward, pour your cake batter evenly into your prepared 9-inch cake pans. Keep in mind that you may weigh them. Doing this ensures that they are even. Next, bake for about 21 to 23 minutes. Or make sure to bake it till the cake cooks thoroughly. With that, to test the doneness of your cake, you can insert a toothpick in the middle of your cake. Because of that, if the toothpick comes out without anything sticking to it, it is ready.
Once your cakes cook well, take them out of the oven. And allow them to cool off completely in the pans. Then transfer them to the cooling wire rack. With that, make sure that your cakes cool completely before frosting and assembling. Finally, set your cakes aside.