coconut cake with coconut filling & buttercream

Ingredients

• FOR THE CAKE:
• 2 tablespoons unsalted butter, at room temperature (for the pans)
• 12 tablespoons cold butter, cut into 12 pieces (for the cake)
• 2 1/4 cups cake flour, plus more for the pans
• 1 cup whole milk, at room temperature
• 6 large egg whites, at room temperature
• 1 - vanilla bean, split lenthwise, seeds scraped out and reserved
• 1/2 teaspoon pure vanilla extract
• 1 3/4 cups granulated sugar
• 1 tablespoon plus 1 teaspoon baking powder
• 1 teaspoon salt
• FOR THE COCONUT FILLING:
• 3/4 cup coconut custard, (below), cold
• 3/4 cup heavy cream, cold
• FOR THE COCONUT BUTTERCREAM:
• 3 sticks unsalted butter, at room temperature
• 1/3 cup confectioners' sugar
• 3/4 cup coconut custard (below)
• 1 pinch salt
• FOR ASSEMBLY:
• - coconut simple syrup (below)
• 2 cups sweetened flaked coconut, lightly toasted, for garnish
• COCONUT CUSTARD:
• 3/4 cup whole milk
• 3/4 cup unsweetened coconut milk
• 1/2 - vanilla bean, seeds scraped out, bean and seeds reserved
• 4 large egg yolks
• 1/3 cup granulated sugar
• 3 tablespoons cornstarch
• 2 teaspoons coconut rum
• 1/2 teaspoon pure vanilla extract
• COCONUT SIMPLE SYRUP:
• 1 tablespoon granulated sugar
• 3/4 cup sweetened flaked coconut