In a stand mixer fitted with a paddle attachment, cream butter and brown sugar together until well-combined.
Stir in egg and egg yolk, pausing to scrape down sides of bowl to ensure that all ingredients are well-incorporated.
Stir in vanilla extract.
In a separate, medium-sized bowl, whisk together flour, pumpkin spice, baking soda, cream of tartar, salt, and cinnamon.
With mixer on low-speed, gradually add flour mixture to wet ingredients until completely combined (scrape down sides and bottom of bowl to completely combine).
Chill dough in refrigerator for 10 minutes. While dough is chilling, stir together sugar and pumpkin spice in a small bowl.
Line a large plate with wax paper. Remove cookie dough from refrigerator and roll into 1 1/2 Tablespoon-sized balls. Roll in sugar/pumpkin spice mixture and place on prepared plate.
Chill in refrigerator at least 30 minutes.
Preheat oven to 350F (177C) and line cookie sheets with parchment paper.
Place dough balls on cookie sheet at least 2" apart and bake on 350F (177C) 10-12 minutes
Allow cookies to cool on cookie sheet for 5 minutes before transferring to cooling rack to cool completely.