Place the oatmeal and milk in a medium saucepan over medium-high heat and bring to a rapid simmer. Reduce the heat to medium-low and cook, stirring constantly, until the oatmeal is thick, about 10 minutes. Add sugar and cinnamon to taste and set the oatmeal aside to cool slightly.
Transfer the oatmeal to a container and refrigerate for at least 2 hours or overnight. Strain the liquid, add the vanilla (if using), and add more milk if you want it thinner. Serve cold.