Combine everything but the vanilla in a pot; to prevent lumps, stir the cornstarch, if you're using it, into the sugar first, or stir it into a bit of the cold milk. If you do use cornstarch you'll need to bring it to a simmer for a minute to reach its full thickening potential and prevent any starchiness. The great thing about rice pudding is that you can add milk in splashes, cook it until it absorbs, add more, and so on until you get the consistency you want. Even so, the next morning it will likely have thickened and need to be loosened up with a little more milk or cream.

Cook, stirring often, until the mixture is as thick as you like, adding more milk if you want. At the end, stir in the vanilla.

Cool.