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1
Make the cake: Preheat the oven to 350 degrees F. Butter and flour two 9-inch-by-2-inch round cake pans and line the bottoms with parchment paper.
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2
Whisk together the milk, egg whites, vanilla seeds and vanilla extract in a medium bowl.
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3
In the bowl of a stand mixer fitted with the paddle attachment, mix together the 2 1/4 cups flour, the sugar, baking powder and salt.
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4
With the mixer running on low speed, add the 12 tablespoons butter, one piece at a time, and continue beating until the mixture resembles moist crumbs.
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5
Add all but 1/2 cup of the milk mixture and beat on medium speed until pale and fluffy, about 1 1/2 minutes.
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6
With the mixer on low speed, add the remaining 1/2 cup milk mixture.
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7
Increase the speed to medium and beat for 30 seconds more.
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8
Scrape the sides of the bowl and mix for 20 seconds longer.
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9
Divide the batter evenly between the cake pans and smooth the tops with a rubber spatula.
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10
Bake until a toothpick inserted into the center comes out with a few crumbs attached, 22 to 24 minutes.
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11
Cool in the pans on a baking rack for 10 minutes.
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12
Run a small knife around the sides of the pans and invert the cakes onto the baking rack.
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13
Remove the parchment paper and let cool completely, about 45 minutes.
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14
Make the coconut filling: Combine the coconut custard and cream in a bowl and whip until soft peaks form.
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15
Make the coconut buttercream: Beat the butter and confectioners' sugar in a stand mixer fitted with the paddle attachment until light and fluffy, about 4 minutes.
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16
Add the coconut custard and salt; beat until the buttercream is smooth.
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17
Assemble the cake: Use a long serrated knife to slice each cake horizontally into 2 layers.
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18
Reserve one of the flat bottom layers for the top of the cake.
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19
Place another one of the layers on a cardboard round, cut-side up, and brush with some of the coconut simple syrup.
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20
Spoon one-third of the coconut filling onto the cake, and using a small offset metal spatula, spread it into an even layer, leaving a 1/2-inch border around the edge of the cake.
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21
Repeat with 2 more layers.
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22
Brush the cut side of the reserved cake layer with the remaining syrup.
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23
Place the layer, cut-side down, on top of the cake.
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24
Frost the sides and the top of the cake with the buttercream.
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25
Pat the toasted coconut onto the sides of the cake and sprinkle some on the top.
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26
Photograph by Yunhee Kim