Preheat the oven to 350°F. Grease 2 (9-inch) round cake pans with butter or nonstick cooking spray. Line the bottom with parchment paper and grease. Lightly flour the pans; set aside.

In a large bowl using an electric mixer on medium speed, cream the butter and sugar together until light and fluffy. Add the eggs, one at a time, beating well after each before adding the next one.

Sift the flour one more time, adding the baking powder. Add it in thirds to the batter, alternating with the coconut milk and beating well after each addition. Beat in the extracts.

Divide the batter evenly between the two pans, and gently tap the bottoms against the countertop to get rid of any air bubbles. Bake until a cake tester inserted in the center comes out clean, about 30 minutes. Remove from the oven and let the cakes cool in the pans at least 10 minutes, then invert the pans onto greased wire racks. Remove and discard the parchment paper, then turn the cakes over and let them cool completely before frosting.

Set one layer on a cake plate and cover evenly with 3⁄4 to 1 cup of the frosting. Set the other layer on top and use the remaining frosting to ice the top and side of the cake. Cover the top and side of the cake evenly with the coconut flakes. This cake does not require refrigeration.

*Note: To toast coconut, spread it over a parchment paper-lined baking sheet. Bake in a preheated 325°F oven until golden brown, 5 to 7 minutes. Check on it regularly to see that it is browning evenly and stir a few times. Sweetened coconut flakes will brown a little faster than unsweetened. Let cool completely before using.