Melt butter in a light-colored saucepan over medium heat.
Continue cooking until it foams and the milk solids become golden brown and nutty.
Immediately transfer brown butter and browned milk solids to a heat-safe bowl.
Cool for 15–20 minutes.
Blot pumpkin puree with paper towels until noticeably thicker.
Whisk flour, cream of tartar, baking soda, cinnamon, pumpkin pie spice, and salt together.
Whisk brown sugar and granulated sugar into the cooled brown butter.
Add egg yolk and mix well.
Mix in the blotted pumpkin and vanilla.
Fold the dry ingredients into the wet mixture just until a dough forms.
Cover and chill for 30–45 minutes.
Preheat oven to 350°F (175°C).
Line baking sheets with parchment.
Combine the coating sugar and cinnamon in a shallow bowl.
Portion approximately 1½ tablespoons dough per cookie.
Gently roll into balls.
Roll each ball in cinnamon sugar.
Arrange approximately 2 inches apart on the prepared baking sheets.
Bake for 10–12 minutes until the edges are set and centers remain slightly soft.
Cool on the baking sheet for approximately 5 minutes.
Transfer to a wire rack to finish cooling.