- Position a rack in the lower third of the oven and preheat the oven to 350 degrees. Butter two 9×2-inch round cake pans and dust with flour, shaking out all of the excess.
- Sift together flour, baking soda, baking powder, and salt thoroughly in a mixing bowl and set aside. In a large measuring cup or another bowl, stir together the cream of coconut, water, and vanilla extract.
- In the bowl of a stand mixer (or a medium mixing bowl if using a hand-held mixer), cream the butter and sugar together on medium-high speed for 3−5 minutes until light yellow and fluffy. Add the eggs one at a time, turning off the mixer to scrape down the bowl with a rubber spatula as you mix each one.
- With the mixer on low speed, add the flour mixture in thirds, alternating with the coconut milk mixture, beginning and ending with the dry ingredients until just combined, scraping down the bowl with a rubber spatula to make sure that the batter is completely incorporated.
- Divide the batter evenly between the prepared pans and smooth the tops with a spatula. Tap the pans firmly on the countertop to make sure any air bubbles are removed from the batter. Bake the cake for 45−50 minutes or until a cake tester inserted in the center comes out clean. Set aside to cool for at least 20 minutes before unmolding. Once the cakes are cool enough to handle, remove them from the pans and transfer them onto a baking rack to cool completely.
For the Frosting
- Combine the flour, ½ cup of milk, vanilla, and cream of coconut in a small saucepan and whisk until blended. Set the pan over medium heat and gradually add the remaining 1 ½ cups milk, whisking constantly. Cook the mixture, whisking until it comes to a low boil, then reduce the heat to low and continue to whisk until the mixture begins to thicken and starts to “burp,” about 2−3 minutes.
- Transfer the mixture to a small heat-proof bowl and stir occasionally as it cools to keep it free of lumps. (If you get a few lumps don’t worry—you can whisk the mixture to dissolve the lumps or pass it thru a fine-mesh sieve.) Set the mixture aside to cool to room temperature. (You can put it in the refrigerator for 10 minutes to speed up the process.)
- In the bowl of a stand mixer fitted with the whisk attachment (or a large bowl using a hand-held mixer) whip the butter on medium speed until soft and creamy, 2−3 minutes. Gradually add the confectioners sugar and beat on high speed until light and fluffy, 5−7 minutes.
- Gradually add the milk mixture, then increase the speed to medium-high and whip until the frosting is light and fluffy, scraping down the bottom and sides of the bowl as necessary with a rubber spatula to make sure the frosting is thoroughly mixed.
To assemble cake
- Level the top of one of the layers with a serrated knife so it sits flat on a serving plate. Place the layer on a flat serving plate with the cut side down.
- With an offset spatula spread the top with a big dollop of frosting. Sprinkle about ½ cup of coconut on top. Place the un-cut layer top side up and with an offset spatula frost the top and sides with frosting, making swirls. Sprinkle coconut on top of the cake and press it into the sides.
- Store the cake in an airtight container at room temperature for up to 2 days.