Combine the water and sugar in a medium saucepan; bring to a boil, stirring until sugar dissolves. Add vanilla bean and cinnamon. Cover, reduce heat, and simmer 15 minutes.
Peel and core pears, leaving stems intact. Cut about 1/4-inch from the base of each pear so they will sit flat. Add pears to sugar mixture. Cover and cook over medium heat 10 minutes or until tender. Remove pears with a slotted spoon; chill thoroughly. Discard the cinnamon stick. Scrape seeds from vanilla bean, and stir seeds into sugar mixture. Discard bean. Set aside 2 cups sugar mixture; reserve remaining mixture for another use.
Return 2 cups sugar mixture to pan; bring to a boil over high heat. Cook until slightly syrupy and reduced to 1/2 cup (about 12 minutes). Chill thoroughly. Serve sauce with pears at room temperature or chilled.