For the cake: Heat the oven to 350ºF. Lightly spray 2 (9-inch) round cake pans with nonstick spray. Line the bottom of each pan with a parchment paper circle. Lightly spray the parchment pieces with nonstick spray. Set aside.
Place the flour, baking powder, and salt into a large mixing bowl and whisk to combine.
Combine the coconut milk and coconut cream in small bowl and set aside.
Place the butter into the bowl of a stand mixer fitted with the paddle attachment and cream on medium speed until fluffy, approximately 1 minute. Decrease speed to low and gradually add the sugar slowly over 1 to 2 minutes. Once all of the sugar has been added, stop the mixer and scrape down the sides. Turn the mixer to medium and continue creaming until the mixture noticeably lightens in texture and increases slightly in volume, 2 to 3 minutes. Stir in the coconut extract.
With the mixer on low speed, add the flour mixture alternately with the coconut milk mixture to the butter and sugar in 3 batches, ending with the milk mixture. Do not overmix.
In a separate bowl, whisk the egg whites until they form stiff peaks. Fold the egg whites into the batter until just combined. Divide the batter evenly between the pans. Bang the pans on the countertop several times to remove any air and to distribute the batter evenly in the pan. Bake on the middle rack of the oven until the cake is light golden in color and reaches an internal temperature of 200ºF, about 40 minutes.
Cool the cake in the pans for 10 minutes, then remove and transfer to a wire rack to finish cooling. Once the cakes have cooled completely, cut across the equator of each to form 4 layers. Place the coconut water into a small spritz bottle and spray evenly onto the cut side of the 4 layers. If you do not have a spritz bottle, you may brush the coconut water on with a silicone pastry brush. Allow to sit while preparing the frosting.
For the frosting: Bring 1 quart of water to a boil in a 4-quart saucepan over high heat. Decrease heat to medium to maintain a steady simmer. In the meantime, place the egg whites, sugar, coconut water, cream of tartar, and salt into a medium size-mixing bowl. Place the bowl over the simmering water and immediately begin beating with an electric hand mixer set to low speed. Beat for 1 minute, then increase the speed to high and continue to beat for 5 minutes. Remove from the heat and beat in the coconut and vanilla extracts for 1 minute. Allow the frosting to sit for 5 minutes before using.
Place approximately 3/4 cup of the frosting on the first layer of cake, sprinkle with 1/2 cup coconut, and top with the next layer. Repeat until you reach the top layer. Frost the top and sides of the cake and sprinkle with the remaining coconut. Refrigerate for at least 30 minutes before serving.