Brown the butter in a saucepan over medium heat, swirling occasionally for 5 to 6 minutes until frothy with amber-brown flecks and a nutty aroma. Pour into a bowl and let cool for 20 minutes.

Spread pumpkin puree onto a triple layer of paper towels and press gently to absorb excess moisture, reducing volume from 1/2 cup to about 1/3 cup concentrated puree.

In a large bowl, whisk the cooled brown butter, brown sugar, and granulated sugar until smooth. Whisk in the blotted pumpkin puree, egg yolk, and vanilla extract until glossy.

In a separate bowl, whisk together flour, cream of tartar, baking soda, cinnamon, pumpkin pie spice, and salt. Fold dry ingredients into wet ingredients with a spatula just until a soft dough forms. Chill dough for 30 minutes.

Preheat oven to 350°F (175°C) and line two large baking sheets with parchment paper. In a small bowl, mix granulated sugar and cinnamon for the coating.

Scoop 2-tablespoon portions of chilled dough, roll into smooth balls, and coat generously in the cinnamon sugar mixture. Place 2 inches apart on prepared sheets.

Bake for 9 to 11 minutes until edges are set and golden with crackled tops, but centers remain soft. Tap baking sheet gently on counter for crinkly rings, let cool on sheet for 8 minutes, then transfer to a wire rack.