Chocolate Layer Cake With Milk Chocolate Frosting

Ingredients

• 2 cups all-purpose flour
• 2/3 cup unsweetened cocoa powder (not dutch-process)
• 1 1/2 teaspoons baking soda
• 1/2 teaspoon salt
• 2 sticks (1 cup) unsalted butter, softened
• 1 cup packed dark brown sugar
• 3/4 cup granulated sugar
• 4 large eggs at room temperature for 30 minutes
• 2 oz unsweetened chocolate, melted and cooled
• 1 1/2 teaspoons vanilla
• 1 1/2 cups well-shaken buttermilk
• 2/3 cup whole milk
• 3 large egg yolks
• 1 tablespoon plus 1 teaspoon all-purpose flour
• 1 1/3 cups confectioners sugar
• 1 teaspoon vanilla
• 3 sticks (1 1/2 cups) unsalted butter, cut into tablespoon pieces and softened
• 8 oz milk chocolate, melted and cooled
• 2 oz unsweetened chocolate, melted and cooled