Coconut-Lime Cake

INGREDIENTS

• 3 1/4 cups cake flour
• 1 Tbs. baking powder
• 3/4 tsp. salt
• 1 3/4 cups milk
• 1 Tbs. vanilla extract
• 16 Tbs. (2 sticks) unsalted butter
• 2 cups sugar
• 1 Tbs. finely chopped lime zest
• 4 eggs
• 4 egg whites
• 1 1/3 cups sugar
• 1/2 cup light corn syrup
• 1/8 tsp. salt
• 1 tsp. vanilla extract
• 2 1/2 cups sweetened shredded coconut