Preheat the oven to 350°F and set an oven rack in the middle position. Spray two 9-inch round cake pans with nonstick spray with flour. Line the bottoms of the pans with parchment paper circles; lightly spray the parchment.

In a large liquid measuring cup or bowl with a pouring spout, whisk together the coconut milk, egg whites, vanilla extract, and coconut extract.

In the bowl of a stand mixer fitted with the paddle attachment or beaters, combine the flour, sugar, baking powder, and salt. Mix on low speed for about 30 seconds to combine. Add the butter and continue mixing on low until the mixture is crumbly and moistened, about 2 minutes. Add the coconut milk and egg white mixture in 3 separate additions, mixing on medium speed for about 2 minutes after each addition, scraping down the sides of the bowl as necessary.

Divide the batter evenly between the prepared pans. Bake for 25 to 30 minutes, or until lightly golden and a cake tester inserted into the center comes out clean. Let cool in the pans on a rack for 15 minutes, then invert onto the rack to cool completely.

In the bowl of a stand mixer fitted with the paddle attachment or beaters, combine the cream cheese, butter, vanilla extract, coconut extract, and salt. Mix on low speed until combined, then increase the speed to medium-high and beat until aerated and light, about 2 minutes. Gradually add the confectioners' sugar, mixing on low to combine. Once all of the sugar is mixed in, increase the speed to medium-high and beat until fluffy, about 1 minute.

After the cake layers have completely cooled, assemble and frost the cake: place 1 layer on a flat serving plate, top side down, and spread with a third of the frosting. Place the second layer on top, top side up, and frost the top and sides with the remaining frosting. Sprinkle the top of the cake with coconut and lightly press more coconut onto the sides. The cake keeps nicely for up to 3 days stored under a cake dome in the refrigerator. Bring to room temperature before serving.

Freezer-Friendly Instructions: The cake layers can be frozen, without frosting, for up to 3 months. After they are completely cooled, double-wrap them securely with aluminum foil or plastic freezer wrap, or place in heavy-duty freezer bag. Thaw overnight on the countertop and then frost before serving.