Melt butter in a light-colored saucepan over medium heat. Swirl occasionally for 4 to 5 minutes as it foams, crackles, and turns deep amber with nutty toasted milk solids. Pour into a heatproof bowl and let cool for 15 minutes.

Spread ⅓ cup of pumpkin puree onto a triple layer of paper towels. Press gently with additional paper towels on top to absorb excess water until reduced to ¼ cup of dense, concentrated pumpkin paste.

In a large mixing bowl, whisk the cooled brown butter, brown sugar, and granulated sugar vigorously for 1 minute until glossy and combined. Whisk in the blotted pumpkin puree, egg yolk, and vanilla bean paste until silky smooth.

Add the all-purpose flour, cream of tartar, baking soda, pumpkin pie spice, and sea salt. Fold with a rubber spatula just until no dry flour streaks remain. Do not overmix.

Cover the bowl with plastic wrap and chill in the refrigerator for 30 minutes to firm up the brown butter fats and make rolling easy.

Preheat oven to 350°F (175°C). Line two large baking sheets with parchment paper. In a small bowl, stir together the rolling coating of granulated sugar, cinnamon, and pumpkin pie spice.

Scoop dough using a 1.5-tablespoon cookie scoop and roll into smooth, round balls between your palms. Roll each ball generously through the cinnamon-sugar mixture until heavily coated.

Place balls 2 inches apart on prepared baking sheets. Bake at 350°F (175°C) for 9 to 11 minutes. The edges should look set and crinkled, while the centers remain soft and puffed.

Immediately upon removing the pan from the oven, firmly tap the baking sheet against the kitchen counter twice. This collapses the puffed center, creating dramatic crinkles and locking in that dense, chewy fudge-like interior!

Let cookies cool on the hot baking sheet for 8 minutes to firm up, then transfer to a wire cooling rack. Enjoy warm with a glass of milk or chai latte!