In a large saucepan, whisk together the sugar, cocoa powder, cornstarch, and salt until well combined.

Gradually pour the milk into the saucepan with the dry ingredients, making sure to whisk well until the mixture is fully combined.

Place the saucepan over medium heat and bring to a boil, stirring or whisking the mixture often (I suggest using a rubber spatula to scrape around the bottom and sides of the pan occasionally). Allow to boil for one minute, the mixture should be thicker and coat the back of a spoon or rubber spatula at this point.

Remove from the heat and stir in the butter, one tablespoon at a time, then stir in the vanilla extract.

Strain the mixture through a fine-mesh strainer into a heat-proof bowl. This is optional, but it does help to remove any lumps that may have formed while the pudding was cooking.

Cover with plastic wrap, placing the plastic wrap directly on the surface of the pudding to prevent it from forming a skin. Allow to cool to room temperature, about 2 hours, then refrigerate for 2 to 3 hours or until thoroughly chilled.

Serve as is, or top with whipped cream and your favorite toppings!