How to Make It
Make cake: Place a rack in center of oven and preheat to 350ºF. Grease and flour 2 9-inch round cake pans.
In a bowl, whisk flour, baking soda, baking powder and salt. Using an electric mixer on medium-high speed, beat butter and sugar until light, about 3 minutes. Beat in eggs 1 at a time. Reduce speed to low; beat in half of flour mixture. Beat in coconut milk and extract, then beat in remaining flour mixture until just combined. Divide batter between cake pans and bake until a toothpick inserted into center comes out clean, about 30 minutes. Let cakes cool in pans on wire racks for 10 minutes. Turn out onto racks to cool completely.
Make frosting: Using an electric mixer on medium-high speed, beat butter until light, 2 to 3 minutes. Reduce mixer speed to low and gradually beat in sugar until fully incorporated. Beat in extracts. Chill 15 minutes.
Assemble cake: Place 1 cake layer on a serving platter. Spread with 1 1/2 cups frosting. Sprinkle with 1/2 cup coconut. Top with second cake layer. Spread remaining frosting on top and sides. Sprinkle remaining coconut over top and sides of cake, pressing to adhere. Chill for at least 2 hours and up to a day. Remove from refrigerator 30 minutes before serving.