Combine the water, sugar and cinnamon in a heavy large sauce pan. Scrape the seeds from the vanilla bean into the sugar-water mixture, and also add the empty vanilla bean. Bring to a simmer over medium-high heat. Meanwhile, using a melon baller, remove the core from the bottom end of the pears. Place the pears into the syrup and simmer until the pears are tender, about 25 minutes.
Allow the pears to cool slightly in the cooking liquid so you can handle them, Transfer the pears to a platter. Reserve the liquid for another use but keep about 1/2 a cup in the pot. Simmer the 1/2 cup syrup over medium-high heat until it thickens slightly, about 5-10 minutes and let cool slightly. It will thicken more as it cools. You want it very-warm but if its too hot it will destroy your ice cream.
Spoon a scoop of ice cream alongside each pear. Drizzle some of the thickened syrup over and around the pears and serve.