In a large mixing bowl, cream together the softened butter, granulated sugar, and brown sugar until light and fluffy.
Mix in the egg, vanilla extract, and pumpkin purée until well combined.
In a separate bowl, whisk together the flour, pumpkin pie spice, salt, baking powder, and baking soda.
Gradually add the dry ingredients to the wet ingredients, mixing until just combined to form a soft dough.
Drop tablespoonfuls of dough onto a parchment-lined baking sheet, spacing them about 2 inches apart.
Bake in a preheated oven at 350°F for 11 minutes, or until the edges are lightly golden.
Allow to cool on the baking sheet for 2 minutes before transferring to a wire rack to cool completely.
Once cool, drizzle with icing if desired.