Preheat your oven to 325 degrees F. Spray three 8-inch or four 6-inch pans with nonstick spray, line the bottom with parchment paper and spray again. Set aside.
In a medium size mixing bowl, whisk the cake flour, baking powder, and salt. Set aside.
In the bowl of a stand mixer fitted with the paddle attachment, cream the butter and the sugar together on medium-high speed for 2 to 3 minutes. The mixture should be light, fluffy, and smooth.
Gradually add the egg whites and whole eggs, making sure to scrape down the sides and the bottom of the bowl between additions. Mix on medium-high for 2 minutes after all the eggs are added. The mixture should be smooth, light in color, and nearly doubled in volume.
Add the coconut extract and vanilla extract.
Turn the mixer on low speed and alternately add the flour mixture and the coconut milk, starting and ending with the flour mixture. Mix until combined. Using a spatula, scrape down the sides and bottom of the bowl and fold the batter a few times.
Evenly distribute the batter in your pans, about 16 ounces in each 8-inch pan and about 12 ounces in each 6-inch pan.
Bake for about 23-25 minutes, or until a toothpick inserted in the center of the cake comes out with a few moist crumbs on it. Remember, the cake continues to bake in the pan for about 5 minutes while it's cooling.
Let cool in pans for 15 minutes and then invert onto cooling racks to cool completely.