Preheat oven to 400°F. Beat cream cheese, egg, 2 tablespoons of the granulated sugar, cornstarch and 1 teaspoon of the vanilla in large bowl with electric mixer on medium speed until smooth. Set aside. Mix pumpkin, remaining 2 tablespoons granulated sugar and pumpkin pie spice blend extract in small bowl until well blended.
Unfold puff pastry sheets on lightly floured surface. Cut strips 1 inch apart and 1 1/2 inches across down long sides of each pastry sheet. Spread 1/2 of the cream cheese mixture down center of each pastry sheet. Top each with 1/2 of the pumpkin mixture. Fold over 1 pastry strip at a time, alternating sides, to enclose filling. Place pastries on baking sheet.
Bake 25 to 30 minutes or until pastry is golden brown. Cool on baking sheet 5 minutes. Remove to wire rack. Cool completely. For the glaze, mix confectioners’ sugar, water and remaining 1/2 teaspoon vanilla until smooth. Drizzle over each pastry. Store leftover pastries in refrigerator.