In a medium saucepan, whisk together the sugar, cocoa, cornstarch and salt. Gradually whisk in the milk until smooth, then whisk in the cream. Set the pan over medium heat and cook, whisking constantly, until the mixture thickens and comes to a boil, about 5 minutes. Continue to whisk and boil for 1 minute.
Remove the pan from the heat and add the chocolate chips and vanilla. Let stand until the chocolate is melted, about 5 minutes, then stir gently until the pudding is smooth.
Divide the pudding among 6 small dessert dishes. Let cool for about 20 minutes to serve warm and soft, or cover and refrigerate for at least 30 minutes or up to 8 hours to serve chilled and firm. Serve with whipped cream.