I've been making this recipe on cold and rainy days for years. It's really more of a traditional Arroz con Leche than a real "pudding" (because of its lack of eggs), but it's delicious. Be warned: you will need to stand over the stove, stirring, for about 45 minutes, to keep the milk from burning.
1 C arborio or short grain rice
3 C milk
1 cinnamon stick
1/2 vanilla pod (or 1 tsp vanilla extract)
1/2 C sugar
Combine the rice, milk, cinnamon and vanilla in a pot and bring to a boil. Reduce the heat to a simmer, and stir constantly until the rice is soft, and most of the liquid has been absorbed. If you need more liquid, you can add more milk or water. Once the pudding has reached the desired consistency, stir in the sugar. Top with a sprinkling of cinnamon.