Chocolate Sandwich Cookie Cake

Ingredients

• 1/2 cup cocoa powder, plus more for dusting
• 7 oz. bittersweet chocolate, broken into pieces
• 14 tbs. (1 3/4 sticks) unsalted butter, cut into cubes
• 1 cup all-purpose flour
• 1 tsp. baking powder
• 3/4 tsp. salt
• 1 3/4 cups granulated sugar
• 4 eggs
• 1 3/4 tsp. vanilla extract
• 4 1/2 cups confectioners' sugar
• 12 tbs. (1 1/2 sticks) unsalted butter
• 3 1/2 tbs. milk, plus more, if needed
• 1 1/2 tsp. vanilla extract
• pinch of kosher salt