Whisk the egg yolks, sugar, cornstarch, cocoa and salt together in a medium bowl and set aside. Bring the milk to a boil in a medium saucepan. Remove from the heat and whisk a little at a time into the egg mixture being careful not to cook the eggs. Once the bottom of the bowl is warm, slowly whisk in the remaining hot milk. Pour the mixture back into a clean medium saucepan (cleaning the saucepan prevents the pudding from scorching), add the vanilla and whisk over medium-low heat until it thickens, 3 to 4 minutes. Cook while constantly whisking until the pudding is glossy and quite thick, 1 to 2 minutes longer. Transfer the pudding to a clean bowl.

Add the chopped chocolate and butter and gently whisk until the chocolate is completely incorporated. Press a piece of plastic wrap onto the surface of the pudding to prevent a skin from forming. Refrigerate for 4 hours.

Before serving, whisk the pudding until it is soft and smooth, about 30 seconds. Divide into custard cups or martini glasses and serve. The pudding will keep in the refrigerator for up to 3 days, with plastic wrap intact.