In a saucepan, whisk together the sugar, cornstarch, salt, and cocoa powder.
Add the milk and the cream and whisk. Cook the mixture over medium high heat whisking constantly.
When the mixture comes to a boil, let it boil for 2 minutes. The mixture will become really thick. Take it off the heat.
Put the chocolate chips in the bottom of a large bowl. Set out 6 ramekins.
Pour the chocolate mixture over the chips.
Add the vanilla. Whisk constantly until the chocolate has melted.
Pour the pudding into the ramekins.
Cover the tops of the pudding with plastic wrap or wax paper. Put the plastic wrap directly on the pudding to avoid getting a skin. Chill in the fridge for at least 2 hours before you serve the chocolate pudding.