Brown the Butter: In a light-colored saucepan over medium heat, melt the butter. Continue cooking, swirling the pan frequently, until the butter foams up and then subsides, leaving nutty-smelling, golden-brown specks on the bottom. Immediately pour the browned butter (scraping up all the brown bits) into a large mixing bowl to stop the cooking. Let it cool for 15 minutes.
Blot the Pumpkin: While the butter cools, spread the pumpkin purée in a thin layer between several sheets of paper towels. Press gently and let sit for 5 minutes to absorb excess water. This is a critical step for a chewy texture.
Mix the Dough: To the bowl with the cooled browned butter, add the packed dark brown sugar and maple syrup. Whisk vigorously until combined. Add the single egg yolk and whisk until the mixture is glossy and smooth. Whisk in the blotted pumpkin, vanilla extract, and maple extract.
Combine Dry Ingredients: In a separate medium bowl, whisk together the flour, 2 tsp pumpkin pie spice, baking soda, baking powder, and salt.
Finish the Dough & Chill: Add the dry ingredients to the wet ingredients and fold together with a spatula until just combined. Do not overmix. Cover the bowl tightly with plastic wrap and chill in the refrigerator for at least 8 hours, or overnight. This step is mandatory.
Prep for Baking: When ready to bake, preheat your oven to 350°F (175°C). Line two large baking sheets with parchment paper. In a small bowl, mix the granulated sugar and ½ tsp pumpkin pie spice for the rolling coat.
Scoop and Roll: Remove the chilled dough from the fridge. Using a medium cookie scoop (about 1.5 tablespoons), portion the dough into balls. Roll each ball between your hands until smooth, then roll generously in the spiced sugar mixture. Place the dough balls 2-3 inches apart on the prepared baking sheets.
Bake & Pan-Bang: Bake for 10 minutes. The cookies will look puffy. Open the oven, lift the baking sheet a few inches, and bang it firmly down on the oven rack 2-3 times. This collapses the center and creates a dense, wrinkly texture.
Finish Baking: Return the cookies to the oven and bake for another 2-4 minutes, or until the edges are set and golden.
Cool: Let the cookies cool on the baking sheet for 10 minutes. They will continue to set and develop their chewy, wrinkled texture. Afterwards, transfer them to a wire rack to cool completely.