Prep: Preheat oven to 350 degrees. Line baking sheets with parchment.
Dry Ingredients: In a medium bowl, whisk together flours, baking soda, cream of tartar, pumpkin pie spice, cinnamon, and salt.
Cream Butter + Sugars: In a large bowl with an electric mixer, beat butter, granulated sugar, and brown sugar on medium speed until light and fluffy, about 2 minutes.
Add Wet Ingredients: Beat in oil, pumpkin puree, egg, and vanilla, scraping down the sides of the bowl as needed.
Combine: Reduce mixer speed to low and gradually add dry ingredients. Mix until just combined. Dough will be soft.
Chill: Cover and refrigerate dough for 20–30 minutes to firm slightly for easier scooping.
Shape: Use a medium cookie scoop to portion dough onto prepared sheets, spacing about 2 inches apart. (If desired, gently flatten tops with the bottom of a glass dipped in sugar for uniform shape.)
Bake: Bake 10–12 minutes, until centers are just set and edges look dry. Cookies will stay pale; do not overbake.
Cool: Cool on the baking sheet 5 minutes, then transfer to a wire rack to cool completely.