Place the oats 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, to taste, and set the oatmeal aside to cool slightly.
Transfer the oatmeal to a container and refrigerate it for at least 2 hours or overnight. Strain the liquid, add the vanilla and add more milk if you want it thinner. Serve cold.