Mile-High Chocolate Cake

INGREDIENTS

• 6 sticks (1 1/2 pound) unsalted butter, at room temperature
• 1 cup sugar
• 1 cup packed light brown sugar
• 2 teaspoons baking soda
• 2 1/4 sticks unsalted butter, softened
• 1 tablespoon pure vanilla extract
• 2 cups sour cream
• 1 cup granulated sugar
• 6 tablespoons unsweetened cocoa powder (not Dutch-process)
• 1/4 cup unsweetened cocoa powder (not Dutch-process)
• 4 large eggs, at room temperature 30 minutes
• 1 1/2 teaspoons pure vanilla extract
• 1 1/2 cups whole milk
• 4 ounces fine-quality unsweetened chocolate, finely chopped
• 1/2 teaspoon salt
• 1 teaspoon baking powder
• 5 ounces fine-quality unsweetened chocolate, chopped
• 2 3/4 cups sifted cake flour (not self-rising; sift before measuring)
• 6 tablespoons all-purpose flour