In a large saucepan over high heat, combine the rice, water and salt and bring to a boil.
Add the cinnamon sticks and reduce the heat to medium-low and cook uncovered, stirring once or twice, until the rice is tender, 30 to 35 minutes.
Remove the cinnamon sticks. In a medium bowl mix together the whole milk, evaporated milk, heavy cream, vanilla, sugar and condensed milk.
Pour the mixture over the rice, stir, and reduce the heat to low. Cook for about 20 minutes more stirring occasionally.
Set aside to cool slightly or refrigerate. The rice pudding can be served warm, at room temperature, or cold. To serve: Spoon the rice pudding into bowls.