In a large bowl, whisk together the flour, cream of tartar, baking soda, salt, cinnamon, ginger, nutmeg, and allspice. Set aside.
Using a stand mixer or hand mixer, cream together the butter and sugars until smooth, scraping down the sides of the bowl with a spatula as necessary. Add the pumpkin and mix until well combined. Add the egg and vanilla extract and beat until combined.
Add the dry ingredients and mix until just combined. Don't over mix.
Wrap the cookie dough in plastic wrap or put in a container. Chill the dough for at least 30 to 60 minutes. I prefer to chill the dough for 24 to 48 hours.
When ready to bake, preheat the oven to 350 degrees Line large baking sheets with Silpat baking mats or parchment paper.
In a small bowl, whisk together granulated sugar and cinnamon.
Shape the cookie dough into round balls, about 1 tablespoon per cookie. Roll the cookie dough balls in cinnamon sugar mixture until generously coated. Place on prepared baking sheets, about 2-inches apart.
Bake cookies for 10 to 12 minutes or until cookies are set around the edges but still soft in the center. Remove from the oven and immediately bang the baking sheet on the counter a few times. This will help remove some air pockets and create ripples around the edges. Let the cookies cool on the baking sheet for 5 minutes. Transfer snickerdoodles to a cooling rack and cool completely.
Notes
The snickerdoodles will keep in an air tight container on the counter for up to 4 days. You can also freeze the cookies for up to 2 months.