Preheat oven to 375 degrees. Line baking sheets with parchment paper or a Silpat mat.
In the bowl of a stand mixer, beat butter and sugar on medium-high for 2-3 minutes, until light and fluffy. With mixing speed on low add pumpkin puree, egg then vanilla. Mix until just combined.
In a medium bowl, whisk together flour, soda, cinnamon, cream of tartar, and salt. With mixing speed on low, slowly add dry ingredients to butter mixture. Mix until combined.
Remove bowl from mixer and chill dough for 30 minutes. Once dough is sufficiently chilled, use a standard size cookie scoop to create balls. Roll dough in hands to form balls, then roll into pumpkin spice mixture. Place onto cookie sheet and flatten slightly with the palm of your hand or the bottom of a measuring cup.
Bake for 10-12 minutes, rotating the sheet half way through the baking process. Cookies should look soft and should have slightly firm edges before removing from the oven (don’t over cook them or they will be dry and crumbly). Allow to cool for 2 minutes before pressing a kiss into the center of each cookie.
Let cookies cool on sheet for 3 additional minutes before transferring them to a wire rack to cool completely.