Preheat oven to 400 degrees.
Cream butter and sugar together with an electric mixer or stand mixer with the paddle attachment.
Add egg, vanilla, and pumpkin puree and mix until smooth.
In a separate bowl combine flour, baking soda, cream of tartar, salt, cinnamon, and pumpkin spice.
Add the dry ingredients to the wet ingredients and mix just until cookie dough forms. It will be a soft dough.
Scoop dough using a medium cookie scoop (2 tablespoons) and roll each cookie dough ball in cinnamon and sugar.
Bake on an ungreased (or parchment paper-lined) baking sheet for 6 minutes. Remove the baking sheet from the oven and tap against the counter a few times to flatten the cookies.Return the cookies to the oven and bake for an additional 3-4 minutes.Tap against the counter once more (if necessary). Allow cookies to sit on baking sheets for 2-3 minutes before transferring the cookies to a cooling rack.