In a medium saucepan, mix together the sugar, cornstarch, salt and cinnamon. Add the oat milk and stir until combined. Bring the mixture to a boil over medium-low heat, stirring frequently at the beginning and constantly after the first few minutes. The cinnamon may clump and not disperse at first, but it will as the mixture heats up and you continue stirring. Once the mixture thickens and starts to boil (approximately 10 minutes), remove the saucepan from the heat and stir in the vanilla.

Immediately pour into individual heatproof dishes or a large heatproof bowl. Cover the top with plastic wrap, directly on the surface of the pudding. This will prevent a skin from forming. Once cooled to room temperature, refrigerate at least two hours before serving.