Step 1: Brown the Butter. Place the butter in a medium saucepan over medium heat. Melt the butter, then continue cooking while whisking constantly. The butter will foam, then turn golden brown with dark specks at the bottom. Once it smells nutty, remove it from heat immediately and pour it into a heat-proof bowl. Let it cool for at least 15 minutes.
Step 2: Blot the Pumpkin. Pumpkin puree contains a lot of water which can make cookies too cakey. Spread the pumpkin puree onto a plate and press it firmly with paper towels to soak up excess moisture. You want to remove about 1-2 tablespoons of liquid until the puree is thick and concentrated.
Step 3: Mix Wet Ingredients. In a large bowl, whisk together the cooled browned butter, granulated sugar, and brown sugar until smooth. Add the egg yolk, blotted pumpkin puree, and vanilla extract. Whisk vigorously until the mixture is well combined and slightly lightened in color.
Step 4: Combine Dry Ingredients. In a separate medium bowl, whisk together the flour, baking soda, cream of tartar, pumpkin pie spice, and salt. Gradually add the dry ingredients to the wet ingredients, stirring with a spatula until just combined. Do not overmix the dough.
Step 5: Chill and Prepare. Cover the dough and refrigerate for at least 30 minutes. This makes the dough easier to handle. While the dough chills, preheat your oven to 350°F (175°C) and line two baking sheets with parchment paper. In a small bowl, mix the remaining 1/4 cup sugar with the ground cinnamon.
Step 6: Shape and Bake. Scoop about 1.5 tablespoons of dough and roll it into a ball. Roll the ball generously in the cinnamon-sugar mixture. Place the balls on the prepared baking sheets, spaced 2 inches apart. Bake for 10-12 minutes or until the edges are set. The centers should still look slightly soft. Let them cool on the pan for 10 minutes before moving to a wire rack.