Preheat oven to 350°F. Line two cookie sheets with parchment paper or silpat baking mats.
Cream butter and 3/4 cup sugar with a stand mixer fitted with the paddle attachment (or you may use a hand mixer). Once the mixture is creamed and fluffy, mix in the egg and vanilla extract until smooth, then mix in the baking soda, cream of tartar, pumpkin spice and salt. Slowly mix in flour until the mixture is just combined.
Place remaining 1/3 cup sugar and pumpkin spice in a small bowl and stir.
Scoop 2 tablespoon sized balls of cookie dough and roll them in the cinnamon sugar, then place them 2” apart on the prepared cookie sheets. Bake for 9-11 minutes, or until the bottoms just start to turn golden brown. (These taste better if you err on the side of under rather than over done). Cool at least 5 minutes on cookie sheet before removing.
Store in an airtight container for up to 3 days or freeze for up to 1 month.