Coconut Cake with Lime Curd

INGREDIENTS

• 1 cup shredded fresh coconut (procedure follows) or sweetened  flaked coconut
• 6 large egg yolks
• about 4 cups shaved fresh coconut (procedure follows) or 2 1/2 cups sweetened flaked coconut
• 1 teaspoon salt
• 3/4 cup sugar
• 1 teaspoon freshly grated lime zest
• 1 1/2 cups sugar
• 1/2 cup fresh coconut liquid (from about 3 heavy coconuts without any cracks and containing liquid, (procedure follows) or water
• 1 teaspoon fresh lime juice
• 1 tablespoon baking powder
• 1 3/4 cups sugar
• 3 tablespoons heavy cream
• 5 large eggs
• 1 tablespoon light corn syrup
• 1 cup whole milk
• 3 cups White Lily flour or cake flour (not self-rising)
• 1 1/2 teaspoons vanilla
• 1/2 cup water
• 2 1/2 sticks (1 1/4 cups) unsalted butter, softened
• 2 teaspoons freshly grated lime zest
• 2 large egg whites
• 3/4 stick (6 tablespoons) cold unsalted butter, cut into pieces
• 1/2 cup fresh lime juice