2 sticks (8 ounces) unsalted butter, at room temperature
1 3/4 buttermilk
2 teaspoons vanilla extract
For the Coconut Buttercream:
3 egg whites
1 cup sugar
1/4 cup water
2 1/2 sticks (10 ounces) unsalted butter, at room temperature
2/3 cup unsweetened coconut milk
1 1/2 teaspoons coconut extract
1 can (20 ounces) crushed pineapple in juice (no sugar added)
1 cup sugar
1/4 cup freshly squeezed lime juice
1 one-inch piece of vanilla bean, split in half
2/3 cup light rum (light, amber, or dark, whichever you prefer)
Coconut flakes and thin slice of fresh pineapple, for decoration
Make the cake:
Preheat the oven to 350 degrees F. Butter three 9-inch cake pans. Line the bottom of each pan with a round of parchment or waxed paper and butter the paper.
Sift together the flour, baking soda, baking powder, and salt into a large mixer bowl; whisk gently to combine. Add the brown sugar, butter, and 1 1/2 cups of the buttermilk to the dry ingredients. With the mixer on low, blend to incorporate. Raise the speed to medium and beat until light and fluffy, 2 to 3 minutes.
Whisk the eggs with the remaining 1/4 cup buttermilk and the vanilla and add to the batter in 3 additions, scraping down the sides of the bowl well and beating only long enough to incorporate between additions. Divide the batter among the 3 prepared pans.
Bake for 25 to 28 minutes, or until a cake tester or wooden toothpick inserted in the center comes out clean. Let the layers cool in the pans for 10 minutes; then turn out onto wire racks, carefully peel off the paper liner, and allow to cool completely before filling and frosting.
Make the frosting (Do this right before you are going to use it):
Put the egg white in the bowl of an electric mixer fitted with the whip attachment so they are all ready to go.
Combine the sugar and water in a small heavy saucepan and place over medium heat, stirring to dissolve the sugar. Bring to boil and cook, without stirring, until they syrup reaches the soft-ball stage, 238 degrees F on a candy thermometer.
Beat the egg whites briefly at medium speed. Slowly add the hot syrup in a thin stream, being careful to avoid the beaters. Continue to whip until the meringue has cooled to body temperature.
With the mixer on low speed, gradually add the butter, several tablespoons at a time, and continue to beat until a smooth, fluffy frosting forms.
Add the coconut milk in several additions, scraping down the sides of the bowl well after each addition. Add the coconut extract and mix until smooth.
Combine the crushed pineapple, sugar, and lime juice in a large nonreactive skillet. With the tip of a small knife, scrape the vanilla seeds into the pan; add the pod as well. Warm over medium-low heat, stirring to dissolve the sugar, 2 to 3 minutes.
Raise the heat to medium and simmer, stirring occasionally to prevent scorching, until the juices have almost completely evaporated and the pineapple has a jamlike consistency. Remove from the heat and discard the vanilla pod. Let the pineapple filling cool completely before using. (The filling can be made a day ahead and refrigerated. Let return to room temperature before using.)
To assemble the cake, place one layer, flat side up, on a cake stand or serving plate. Sprinkle a generous 3 tablespoons rum over the cake. Spread half of the pineapple filling over the layer, leaving a 1/4-inch margin around the edge. Add the second layer, sprinkle with more rum, and cover with the remaining filling. Top with the third layer, flat side up, and sprinkle with the remaining rum. Frost the top and sides of the cake with the Coconut Buttercream. Decorate with some coconut shreds and thin slices of pineapple.