Coconut Rum Cake

Ingredients

• 1 1/4 cups all-purpose flour
• 1 1/2 teaspoons baking powder
• 1/4 teaspoon salt
• 4 large eggs plus 3 large yolks
• 1 1/2 cups sugar
• 1 teaspoon pure vanilla extract
• 1 1/2 sticks unsalted butter, melted and cooled
• 3/4 cup well-stirred sweetened cream of coconut such as coco lópez
• 1 medium coconut
• 2 teaspoons confectioners sugar
• 3 tablespoons cream cheese, softened
• 3 tablespoons well-stirred sweetened cream of coconut
• 1 tablespoon dark rum
• 3/4 teaspoon pure vanilla extract
• 2 to 3 tablespoons heavy cream
• 1/2 cup confectioners sugar