In a large saucepan combine pear nectar and cardamom. Bring to boiling. Meanwhile, if desired, peel pears. Cut thin slices from bottoms of pears so they stand upright. Using a melon baller or small spoon, remove cores, starting from the bottom of each pear and leaving stems intact.
Add pears to nectar mixture in saucepan. Reduce heat; simmer, covered, for 5 to 7 minutes or just until pears are tender. Remove pears with a slotted spoon, reserving cooking liquid. Set pears aside to cool. In a small bowl stir together sugar and crystallized ginger; set aside.
Preheat oven to 375 degrees F. On a lightly floured surface, roll pastry into a 12x4-inch rectangle. Using a fluted pastry wheel or pizza cutter, cut rectangle into eight 12x1/2-inch strips. Place the end of one pastry strip at the top of one of the pears. Working down from the top, wrap pastry strip around the pear in a spiral fashion. Add a second strip, pressing onto the end of the first strip. Press end of the last strip firmly onto the pear to secure. Repeat with the remaining pears and the remaining pastry strips. (Strips will spiral about three-fourths of the way down the pear.)
Place pastry-wrapped pears upright on a baking sheet. Brush pastry with a little water and sprinkle lightly with sugar-ginger mixture. Bake for 25 to 30 minutes or until pastry is puffed and golden. Cool for 20 minutes.
Meanwhile, for sauce, in a small bowl combine the 2 tablespoons cold water and cornstarch; stir into cooking liquid in saucepan. If using, add vanilla bean. Cook and stir over medium heat until thickened and bubbly. Cook and stir for 2 minutes more. Remove from heat. Remove vanilla bean, if using, or stir in vanilla. Serve pears with sauce.