Step 1

For the cake: Position racks in the middle and lower third of the oven and preheat to 350 degrees F. Butter three 9-inch round cake pans and line the bottoms with parchment paper; butter the parchment, dust with flour and tap out the excess. Set aside.

Step 2

Whisk the flour, baking powder, baking soda and salt in a medium bowl. Whisk the buttermilk and cream of coconut in a small bowl. Beat the butter and 1 1/4 cups granulated sugar in a large bowl with a mixer on medium-high speed until light and fluffy, about 4 minutes. Add the egg yolks, one at a time, beating well after each addition, then beat in the vanilla and coconut extracts. Reduce the mixer speed to low; beat in the flour mixture in three batches, alternating with the buttermilk mixture, until combined.

Step 3

Beat the egg whites and the remaining 1/2 cup granulated sugar in a large bowl with clean beaters on medium-high speed until stiff glossy peaks form, 4 to 5 minutes. Using a rubber spatula, fold the egg whites into the batter in three batches until just combined (do not overmix). Divide the batter among the prepared pans and bake, switching the pans halfway through, until the cakes are lightly browned and the centers spring back when lightly pressed, 30 to 35 minutes. Transfer to racks and let cool 20 minutes in the pans, then run a small knife around the edges of each cake and carefully invert onto the racks; remove the parchment and let cool completely.

Step 4

For the frosting: Beat the butter and cream cheese in a large bowl with a mixer on medium-high speed until smooth, about 2 minutes. Reduce the mixer speed to low and beat in about half of the confectioners' sugar until combined. Add the remaining confectioners' sugar, salt and vanilla and coconut extracts and beat until combined. Increase the mixer speed to medium high and continue beating, scraping down the sides of the bowl as needed, until light and fluffy, about 3 minutes.

Step 5

Place one cake layer on a cake stand or platter and top with a heaping 2/3 cup frosting. Add another cake layer, more frosting and the last cake layer. Cover the top and sides of the cake with the remaining frosting. Sprinkle the coconut all over the top and sides of the cake, gently pressing to adhere.