The unsweetened coconut is a perfect way to impart more coconut flavor to the cake without more sugar, but sweetened flaked coconut is a fine substitute. The orange blossom simplesyrup adds moistness to the cake and a layer of flavor that enhances the coconut beautifully.
Preheat the oven to 350°F and place a rack in the center position. Coat 3 9-inch cake pans with butter and line the bottoms with parchment circles.
In a stand mixer fitted with the paddle attachment, cream the butter and shortening on high speed until they are light and fluffy. On medium-low speed, add the sugar one cup at a time. Once the sugar is incorporated, increase the speed and beat until the mixture is light and fluffy again, about 3 minutes.
Crack the eggs into a bowl, then add them one at a time to the butter mixture, beating to incorporate each egg before adding the next one.
In a medium bowl, whisk together the flour, baking powder, and salt. In a glass measuring cup, combine the buttermilk, coconut milk, and coconut extract. On low speed, alternate adding the flour mixture and the buttermilk mixture into the batter in several additions, beginning and ending with the dry ingredients. Stop to scrape down the sides of the bowl as you go, and beat just until each is incorporated.
Divide the batter evenly among the three cake pans and smooth the batter into each pan. Bake the cakes for 25 to 30 minutes, or until they are golden, spring back lightly when touched in the center, and a toothpick inserted in the center comes out clean.
While the cakes bake, make the simple syrup: In a small saucepan, bring the sugar, water, and lemon juice to a boil. Reduce the heat and simmer five minutes. Add the orange blossom water and set aside.
When the cakes are done baking, cool in their pans for 10 minutes, then remove the cakes and cool on wire racks. When the cakes are completely cooled, brush the tops and sides with orange blossom simple syrup.
For the Buttercream:
Beat the cream cheese and butter in the bowl of a stand mixer fitted with the paddle attachment, or a large bowl using hand beaters, until smooth. Beat in the coconut extract. Sift in the confectioners' sugar one cup at a time, incorporating on low speed and adding a tablespoon of coconut milk after every cup or two. Beat the buttercream until it is smooth and light.
To assemble the cake, place one layer of cake on a serving platter or cake stand, placing the squared-off cake edge side down. Top it with about a cup of buttercream and spread evenly to the edges. Center the second layer on top of the first layer with buttercream, and top with another cup of buttercream, spreading it evenly to the edges. Center the third cake layer on top, placing the squared-off cake edge side up, and spread the buttercream evenly over the top. Frost the sides of the cake. Sprinkle the coconut over the top and sides of the cake in small handfuls (it’s messy, but that’s okay; just brush the excess coconut from the rim of the cake platter before serving). Serve the cake immediately, or chill and serve within a day or two.
Pat the the coconut onto the top and sides of the cake in small handfuls (it’s messy, but that’s okay; just brush the excess coconut from the rim of the cake platter before serving). Serve the cake immediately, or chill and serve within a day or two after bringing back to room temperature.