In a small saucepan, combine pear nectar and cardamom. Bring to boiling. Meanwhile, cut a thin slice off the bottom of each pear so they can stand upright. Use a melon baller to scoop out the seeds, starting from the bottom of the pear.
Add pears to pear nectar mixture. Cover and cook about 10 minutes or until pears are just tender when pierced with a sharp knife (pears can be on their sides while poaching). Remove pears with a slotted spoon and set aside to cool. Set pear nectar mixture aside.
Preheat oven to 375 degrees F. On a lightly floured surface roll pastry to a 6 x 6-inch square, cut the pastry in half crosswise. Using a fluted pastry wheel, cut pastry into 1/2-inch wide strips.
Place the end of one pastry strip underneath one of the pears. Working up from the bottom, wrap pastry strip around pear in a spiral fashion leaving 1/4 to 1/2 inch between spirals. Add a second strip, pressing onto the end of the first strip; continue wrapping pear. Repeat until pear is wrapped to the top. Press the end of the last strip around the top of the pear to secure. Repeat with remaining pear and pastry strips.
Place pastry wrapped pears on a small baking sheet. Bake for 25 to 30 minutes or until pastry is puffed and golden. Remove from oven; cool about 20 minutes.
Meanwhile, for sauce, in a small bowl combine 1 tablespoon water and the cornstarch until smooth. Add to pear nectar mixture in saucepan. Cook and stir until thickened and bubbly. Cook and stir 2 minutes more. Remove from heat and stir in vanilla.
To serve, place each baked pear in a shallow dessert dish. Spoon sauce around pears.