COMBINE rice, cinnamon stick and water in large bowl; cool. Cover; refrigerate for at least 2 hours, preferably overnight.
REMOVE cinnamon stick. Spoon rice into blender container (reserve soaking water). Cover; blend on High for 3 to 4 minutes until mixture is as smooth as possible. Add the reserved soaking water and sugar; blend for an additional 2 minutes. Strain mixture through a cheesecloth or fine sieve into a pitcher, pressing the rice solids until only a dry paste remains; discard paste. Stir evaporated milk into the mixture.
TO SERVE: Pour into tall glasses with ice cubes; sweeten with additional sugar, if desired. Sprinkle with cinnamon. Garnish with lime rind.