Preheat the oven to 375 degrees F and adjust racks to the middle position. Line 2 cookie sheets with parchment paper.
In a medium bowl, sift together the flour, baking powder, baking soda, cinnamon, ginger, allspice, nutmeg, and salt.
Using a hand held mixer cream together the butter, granulated sugar and the brown sugar until light and fluffy and the volume has increased. Add the egg and the vanilla and mix until incorporated. Stir in the sweet potato puree and blend until smooth. Beat in the dry ingredients in increments and combine well. Stir in the pecans.
Drop by heaping tablespoons onto the prepared cookie sheets, leaving about 2 inches of space between each cookie. Bake until the cookies are lightly golden around the edges and they spring back from the touch, about 18 minutes. Let cool completely on the cookie sheets before glazing.
For the glaze:
Combine the confectioners' sugar, orange juice, and vanilla in a small bowl and stir until smooth. Drizzle over the cookies and let harden for 1 hour before serving.
Cook's Note: If you need to thin the glaze, add more orange juice. If you need to thicken it, add more confectioners' sugar.