Bring the water to a boil in a medium saucepan. Add rice, cover, reduce the heat to low and simmer until the rice is nearly cooked, about 20 minutes.
Preheat oven to 375.
In a large bowl, whisk together the soy milk, sugar, and salt. When the rice is cooked and still hot, add the soy milk mixture and cinnamon stick. Cover, place in the oven and cook for 45 minutes.
Remove from the oven, uncover and remove the cinnamon stick. Stir in the vanilla, cinnamon and nutmeg. The pudding will be slightly liquidy; the liquid will continue to absorb into the rice and thicken as the pudding cools.
Distribute amoung 8 bowls. Serve warm or at room temperature. Dust with brown sugar if desired.
The pudding will keep in the fridge in an airtight container for 3 days.