Position a rack in the lower third of the oven and preheat the oven to 350 degrees Fahrenheit. Butter two 9×2-inch round cake pans and dust with flour, tapping the pans on the counter to shake out the excess.

Sift together the flour, baking soda, baking powder, cardamom, and salt; set aside.

In a large measuring cup or a small bowl, stir together cream of coconut, a quarter cup water, vanilla, and almond extract.

In the bowl of a stand mixer fitted with the paddle attachment (or in a large mixing bowl, using a handheld mixer), cream the butter and sugar together on medium-high speed for three to five minutes, until light and fluffy. Add the eggs one at a time, beating well after each addition and scraping down the sides of the bowl with a rubber spatula as necessary.

With the mixer on low speed, add the flour mixture in thirds, alternating with the cream of coconut mixture and beginning and ending with the flour, mixing just until combined; scrape down the sides of the bowl with a rubber spatula as necessary.

Divide the batter evenly between the prepared pans and smooth the tops with a spatula. Tap the pans firmly on the countertop to remove any air bubbles from the batter.

Bake for 45-50 minutes, until a cake tester inserted in the center of a cake comes out clean. Let cool for 20 minutes, then remove the cakes from the pans and cool completely on a wire rack.

Combine flour, half a cup of milk, vanilla, and coconut extract in a small saucepan and whisk until blended.

Set the pan over medium heat and gradually add the remaining one and a half 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,” two to three minutes.

Transfer the mixture to a small heatproof bowl and stir it occasionally as it cools to keep it lump-free. (If you do get a few lumps, don’t worry – you can whisk the mixture to dissolve the lumps, or pass it through 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 in a large bowl, using a handheld mixer), whip the butter on medium speed until soft and creamy, two to three minutes. Gradually add the confectioners’ sugar and beat on high speed until light and fluffy, five to seven 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. The frosting can be stored in an airtight container at room temperature for up to two days.

Level the top of one of the cake layers with a serrated knife so it is flat. Place the layer cut side down on a flat serving plate. 

With an offset spatula, spread the top of the layer with a big dollop of frosting. Sprinkle about half a cup of the coconut on top.

Place the second layer on top, right side up, and frost the top and sides with the remaining frosting, making swirls with the spatula. Sprinkle some of the remaining coconut on top of the cake and press the rest onto the sides.

The cake can be stored in an airtight container at room temperature for up to two days.