Coconut Layer Cake

Name: Coconut Layer Cake
Prep time: 1 h
Total time: 1 h
Cuisine: American
Ingredients: 3 sticks unsalted butter, at room temperature, plus more for the pans; 1 1/2 c. all-purpose flour, plus more for the pans; 2 3/4 c. cake flour (not self-rising); 1 tbsp. plus 1/4 teaspoon baking powder; 1 1/4 tsp. kosher salt; 2 1/4 c. sugar; 3 large eggs, plus 3 egg whites; 1 tbsp. coconut extract; 1 tsp. vanilla extract; 1 1/2 c. whole milk; 2 c. sugar; 8 large egg whites; 6 sticks unsalted butter, cut into pieces, at room temperature; Pinch of kosher salt; 2 c. sweetened shredded coconut