Preheat oven to 350 degrees Fahrenheit. Line a cookie sheet with parchment paper or use silpat.
In a large mixing bowl, blend together the butter, pumpkin puree and sugar until light and fluffy, about 2 minutes.
Add in the vanilla, cinnamon, ginger, nutmeg, allspice and salt and mix well.
Slowly mix in the flour and until just incorporated.
Fold in the pecan pieces.
Using your hands, shape the dough into 1-inch balls. Place the cookies on the baking sheet, spaced about 1 1/2-inches apart.
Bake for 15 minutes, until bottoms of cookies are lightly browned. Let the cookies cool on the baking sheet for 5 minutes.
Pour the powdered sugar in a large Ziplock bag. Add the cookies in batches to the bag, seal the bag and shake the bag up and down so that the powdered sugar generously covers all of the cookies.
Place the cookies on a wire rack to cool completely.