BLOT THE PUMPKIN: Spread 1 cup of pumpkin puree onto a plate lined with several layers of paper towels. Place more paper towels on top and press down gently to absorb moisture. Repeat this process with fresh paper towels until the pumpkin has reduced in volume to 1/2 cup.
BROWN THE BUTTER: In a medium saucepan over medium heat, melt the butter. Continue cooking, swirling the pan occasionally, until the butter foams, turns a golden amber color, and smells nutty (about 5-7 minutes). Watch closely so it doesn't burn. Pour immediately into a large heat-proof mixing bowl to stop the cooking. Let cool for 10 minutes.
MIX WET INGREDIENTS: Whisk the dark brown sugar and granulated sugar into the slightly cooled brown butter. Whisk in the egg yolk, vanilla extract, and the 1/2 cup of blotted pumpkin puree until smooth and combined.
MIX DRY INGREDIENTS: In a separate medium bowl, whisk together the flour, baking soda, baking powder, pumpkin pie spice, and salt.
COMBINE: Pour the dry ingredients into the wet ingredients. Use a rubber spatula to fold them together just until combined. Do not overmix. Fold in the chocolate chips.
CHILL (MANDATORY): Cover the bowl with plastic wrap and refrigerate for at least 30 minutes. The dough will be sticky and needs this time to firm up so it doesn't over-spread in the oven.
PREHEAT: While the dough chills, preheat your oven to 350°F (175°C). Line baking sheets with parchment paper.
SCOOP: Using a cookie scoop (about 1.5 tablespoons of dough), form balls and place them 2 inches apart on the prepared baking sheets. Roll them briefly in your hands to smooth them, then slightly flatten the tops with your fingers.
BAKE: Bake for 11-13 minutes. The edges should be set and golden brown, but the centers will still look very soft.
COOL: Let the cookies cool directly on the baking sheet for at least 5 minutes. They will deflate slightly and firm up during this time, creating the chewy texture. Transfer to a wire rack to cool completely.