Brown the butter. Melt 113 grams of butter in a medium skillet over medium heat. Stir continuously with a rubber spatula. Keep stirring until the butter achieves a rich amber color and a nutty aroma (this is the sign that it's finished!). Immediately remove the pan from the heat and turn off the burner. Note: Starting with 113 grams of butter will yield approximately 93 grams of brown butter. Let the butter cool. Transfer the browned butter immediately to a large mixing bowl or the bowl of your stand mixer, and let it cool for 20 minutes.
Mix in the sugars. Once the butter has reached the ideal temperature (liquid and slightly warm), add the granulated sugar and dark brown sugar to the bowl and whisk thoroughly to blend.
Prepare the pumpkin purée. Using a food scale, measure 86 grams of pumpkin purée and spread it in a thin, even layer across a paper towel. Blot to absorb moisture, then transfer the purée to a fresh paper towel and repeat the blotting process one or two more times until the purée weighs 60 grams.
Add the remaining wet ingredients. Add the blotted pumpkin, egg yolk, and vanilla extract to the bowl. Mix on medium speed until the ingredients are just combined and the mixture looks smooth and creamy.
Add the dry ingredients. Next, add the gluten-free flour, pumpkin pie spice, cinnamon, baking soda, baking powder, and salt. Use a whisk (or mix on medium speed) until the ingredients are thoroughly blended. Be careful not to overmix the dough. Use a spatula to fold in the chocolate chips until evenly distributed. Cover the bowl and place it in the refrigerator for 30 minutes.
Scoop and roll the dough. After 30 minutes, remove the dough from the refrigerator. Preheat your oven to 350°F. Line two large baking sheets with parchment paper. Using a large cookie scoop or a spoon, portion the chilled dough into precise 57-gram balls, ideally weighing them on a food scale for accuracy. Roll each portion smoothly between your palms, then place 6 of these smooth dough balls onto each prepared baking sheet, ensuring they are spaced well apart to allow for proper spreading.
Bake the cookies. Bake the cookies for 11-12 minutes or until the edges are browned and the center is puffed and slightly cracked. Immediately after removing the tray from the oven, sprinkle flaky sea salt over the tops. For perfectly round cookies, gently use a large cookie cutter to shape them while still warm. Let the cookies rest on the baking sheet for 10 minutes before carefully moving them to a wire rack to cool completely.