Preheat oven to 375°, and spray 2 large baking sheets with cooking spray.
For cookies: Whisk together flour, baking powder, baking soda, five-spice powder, and salt in a medium bowl.
Beat sugar, butter, and zest with an electric mixer on medium speed in a large bowl until light and fluffy. Beat in pumpkin, egg, and vanilla until blended. Reduce speed to low, and beat in the flour mixture just until blended.
Drop cookie dough by rounded teaspoonfuls onto baking sheets. Bake for 12 minutes, or until cookies are lightly browned. Cool 10 minutes on cooling racks.
For glaze: Whisk together all in-gredients in a large bowl until sugar is dissolved. Drizzle glaze evenly over cookies. Let cool until glaze is set.