In a wide skillet pour milk. Bring to a boil. Reduce to a simmer and cook, stirring frequently, until reduce by half, 20 - 30 minutes. Strain into a large saucepan and add the water and cinnamon sticks. Bring to a boil, reduce to a simmer and cook 5 minutes. Remove from the heat and let sit 15 minutes. Remove the cinnamon sticks and reserve. Combine the sugar, rice flour, and vanilla extract in a bowl. Pour in the milk mixture and whisk to incorporate well. Refrigerate at least 4 hours. Then pour the mixture into a pitcher, discarding the sediment that has settled on the bottom of the bowl. Serve cold over ice, with cinnamon sticks as stirrers.
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