Coconut Layer Cake

INGREDIENTS

• 2 1/2 cups all-purpose flour
• 1 teaspoon baking soda
• 1/2 teaspoon baking powder
• 1/2 teaspoon salt
• 2 sticks (1 cup) unsalted butter, at room temperature, cut into pieces
• 2 cups sugar
• 4 large eggs
• 1 cup coconut milk
• 1 teaspoon coconut extract
• 4 sticks (2 cups) unsalted butter, at room temperature
• 8 cups confectioners' sugar, sifted
• 1 tablespoon coconut extract
• 1 teaspoon vanilla extract
• 2 2/3 cups sweetened flaked coconut (1 7-oz. bag)