In a heavy-bottomed, 3-quart saucepan, combine the milk, water, sugar, cinnamon stick, and rice. Stir to combine.

Bring to an intense simmer just below boiling over medium-high heat, stirring often.

Reduce heat to maintain a steady simmer and continue cooking, stirring often until the rice is tender, about 35 to 45 minutes.

Remove from heat and remove the cinnamon stick. Stir in the vanilla bean paste or vanilla extract and raisins, if using.

Spoon the rice pudding into individual ramekins or small containers, or transfer to a large serving dish.

Let the pudding cool slightly before serving or let cool to room temperature, cover tightly and refrigerate until ready to serve, up to 1 day in advance.

Just before serving, top with freshly grated cinnamon or ground cinnamon.