Add 2 cups water to medium, heavy saucepan over medium-high heat. Bring water to boil. Stir in rice and salt. Return water to boil. Reduce heat to low. Cook, covered, until water is absorbed and rice is tender, about 20 minutes
Stir in milk, cinnamon sticks and lemon or orange zest. Increase heat to medium-high; bring milk to boil. Reduce heat to low. Cook, uncovered, stirring occasionally to prevent sticking and scorching, until mixture is thick and creamy, about 25 minutes. Stir in condensed milk and vanilla. Cook, stirring often, until flavor is absorbed, about 5 minutes more.
Pour rice pudding into serving bowl; serve warm or chilled. Sprinkle with cinnamon before serving, if desired.