John's Three-Layer Apple Cake

INGREDIENTS

• 4 large egg whites
• 1 cup packed light-brown sugar
• 1/4 teaspoon salt
• 1 1/2 cups (3 sticks) unsalted butter, room temperature, cut into pieces
• 1/2 cup (1 stick) unsalted butter, melted, plus more for pans
• 2 cups all-purpose flour (spooned and leveled), plus more for pans
• 2 teaspoons baking soda
• 1/2 teaspoon baking powder
• 2 teaspoons ground cinnamon
• 1/2 teaspoon ground ginger
• 3/4 teaspoon salt
• 2 cups packed light-brown sugar
• 2 large eggs
• 4 Granny Smith apples, peeled, two coarsely grated and two diced