Brown the Butter: In a medium saucepan, melt the butter over medium heat. Continue cooking, swirling occasionally, until the butter foams and then turns a golden brown color with a nutty aroma (about 5-7 minutes). Watch carefully to avoid burning. Once browned, remove from heat and let it cool for 10-15 minutes.

Make the Cookie Dough: In a large mixing bowl, whisk together the brown butter, pumpkin puree, and granulated sugar until smooth. Add the egg and vanilla extract and mix until combined. In a separate bowl, whisk together the flour, cream of tartar, baking soda, cinnamon, nutmeg, and salt. Gradually add the dry ingredients to the wet ingredients and mix until just combined. The dough will be soft and slightly sticky.

Chill the Dough: Cover the dough and refrigerate for at least 30 minutes to 1 hour, or until firm. This step helps the cookies keep their shape while baking.

Prepare the Cinnamon Sugar: While the dough chills, combine the 1/4 cup granulated sugar and 1 tablespoon cinnamon in a small bowl. Set aside.

Preheat the Oven: Preheat your oven to 350°F (175°C). Line a baking sheet with parchment paper or a silicone baking mat.

Shape the Cookies: Once the dough has chilled, scoop tablespoon-sized portions of dough and roll them into balls. Roll each ball in the cinnamon-sugar mixture, coating it generously.

Bake: Place the dough balls about 2 inches apart on the prepared baking sheet. Bake for 10-12 minutes, or until the edges are set and slightly golden, and the centers are still soft. Be careful not to overbake; the cookies will continue to firm up as they cool.

Cool: Let the cookies cool on the baking sheet for a few minutes before transferring them to a wire rack to cool completely.