In a medium saucepan over medium heat, combine 6 cups water, rice, cinnamon, peach slices, sugar, and vanilla. Stir to combine. Bring to a boil, reduce to a simmer and cook, covered, for 40 minutes, until rice is tender. Remove from heat and let cool. Discard cinnamon stick and puree in batches in a blender. Strain through a fine mesh strainer into serving pitcher. Discard pulp, and stir in the remaining 2 cups of water. Serve warm or chilled, dusted with ground cinnamon.