In a medium saucepan, stir together cornstarch, cocoa powder, sugar, and salt. Slowly stir in cold milk until combined.

Turn heat to medium and cook, stirring constantly, until mixture comes to a boil. Boil for 1 minute, then remove from heat and stir in butter and vanilla extract.

Place a piece of plastic wrap directly over the pudding, so the pudding doesn’t form a skin on top as it cools. Allow to cool and refrigerate for at least an hour to allow it to set up.