Preheat oven to 325 degrees F. Line the bottom of two 9-inch cake pans with parchment paper. Spray with nonstick cooking spray WITH flour or butter and flour pans.
Beat the egg and egg whites in a medium bowl (or large measuring cup – preferably something with a pouring spout) with a fork to combine. Add the cream of coconut, water, and coconut extract and vanilla extract and beat with a fork until thoroughly combined
Mix the flour, sugar, baking powder and salt in the bowl of a standing mixer at the lowest speed to combine, about 30 seconds. With the mixer still running at the lowest speed, add 1 piece of butter at a time and continue to beat until all the butter is added. Increase speed to medium to medium-high and continue to beat until the mixture resembles coarse meal, with butter bits no larger than small peas (this can take several minutes).
With the mixer running on low, add approximately half of the egg mixture to the flour mixture. Increase speed to medium-high and beat until light and fluffy, about 30 seconds. With the mixer still running, add remaining egg mixture. Stop the mixer and scrape down the bowl then continue to beat at medium-high speed to combine, about 15 seconds (batter will be thick).
Divide the batter between the cake pans and drop a few times on the counter to get rid of air bubbles. Bake at 325 degrees F for 25-30 minutes or until the cakes have pulled away from the sides of the pans and a toothpick inserted in the center of the cakes comes out clean (don’t open oven while baking or cakes could fall in center.)
Cool the cakes in the pan on a wire rack for 10 minutes then loosen cakes from the sides of the pan with a butter knife then invert onto a plate or baking pan then invert back onto the cooking rack so the tops sides face up; cool to room temperature before frosting.