In a medium saucepan, use a wooden spoon to stir together the sugar, cocoa, corn flour and salt. Slowly stir in the Oat Milk and keep stirring until smooth and combined.
Stir the mixture constantly over medium-low heat, scraping the bottom, sides and corners of the pan, until the pudding thickens, begins to bubble, and coats the back of the spoon. This should take about 5 to 10 minutes. (If the pudding is coating the bottom of the pan too quickly, reduce the heat.)
Add the chocolate and stir vigorously until the pudding is very thick and smooth, about 30 seconds longer.
Remove from the heat and stir in the vanilla. Spoon the pudding into a serving bowl or individual ramekins if you have them and serve warm.