CHOCOLATE PUDDING ICEBOX CAKE

Steps:

• In a large saucepan, combine 3 cups milk, half-and-half, 1/2 cup plus 2 tablespoons sugar, salt, and vanilla bean and seeds, if using. Place saucepan over medium-high heat and bring to a simmer.
• Meanwhile, in a large heat-proof bowl, whisk together egg yolks, remaining 1/2 cup plus 2 tablespoons sugar, cocoa, cornstarch, and remaining 3/4 cup milk. Whisking constantly, gradually pour the hot milk mixture into the egg yolk mixture. Set a fine-mesh sieve over saucepan and strain custard mixture back into saucepan. Bring to a boil over medium heat, whisking constantly. Boil, whisking, until mixture thickens to a puddinglike consistency, about 10 seconds. Remove vanilla bean, if using, and discard.
• Transfer custard mixture to the bowl of an electric mixer fitted with the paddle attachment. Add chocolate and beat on medium speed until chocolate is melted and mixture has cooled slightly, 2 to 3 minutes. Beat in vanilla extract, if using. Beat in butter, a little at a time, and continue beating until chocolate is entirely melted and mixture is cool, 5 to 10 minutes more.
• Layer the bottom of an 8-inch-square baking dish with 1/3 of the graham crackers, breaking up crackers as needed to create a snug, even layer. Spoon 1/3 of the pudding mixture on top; smooth top. Repeat process twice using remaining graham crackers and pudding, to create a total of 3 layers of each. Transfer to refrigerator; refrigerate until chilled, 2 to 3 hours.
• In the bowl of an electric mixer fitted with the whisk attachment, beat together heavy cream and confectioners' sugar until medium peaks form. Spread whipped cream over chilled cake and serve.