Bring 2 cups water, the milk, almonds, rice and cinnamon sticks to a boil in a medium saucepan over high heat. Reduce the heat to low, cover and simmer until the rice is tender, about 30 minutes. Remove the cinnamon sticks and cool completely.
Working in batches, if necessary, carefully transfer the mixture to a blender and puree until smooth. Pour into a pitcher. Stir in the sugar and add enough water to make a total of 8 cups. Chill. Serve in tall glasses over ice. Garnish with a sprinkle of cinnamon.