In a large bowl, using an electric hand mixer or in the bowl of a stand mixer cream together butter, ½ cup brown sugar and ¼ cup white sugar until well mixed.
Add in pumpkin puree and vanilla, continue mixing until well blended.
In a separate medium bowl whisk together flour, 1 ½ tsp pumpkin spice, cream of tartar, baking soda and salt until well blended.
Add the flour mixture to the pumpkin mixture gradually, mixing between each addition until all of the dry ingredients have been incorporated into the wet ingredients.
Cover the bowl with plastic wrap or aluminum foil and refrigerate for at least 4 hours.
When ready to bake-
Preheat the oven to 350 and line your cookie sheet with parchment paper.
Stir together the ¼ cup granulated sugar and 2 tsp pumpkin spice in a small bowl or shallow dish
Scoop dough out 1 tablespoon at a time using a spoon or dough scoop and roll into a ball. Place dough ball into the sugar and pumpkin spice mixture and roll around in the cinnamon sugar mixture to cover. Place on your prepared baking sheet.
Continue rolling tablespoons of dough into balls and coating with the sugar mixture, placing them about 2 inches apart on your baking sheet.
Bake for 11-13 minutes or until the top begins to crack.
Allow to cool on the baking sheet for 5 minutes and then move to a wire cooling rack to cool completely.
Store baked cookies in a ziplock bag or other airtight container.