Stack a few paper towels on top of each other. Add pumpkin puree in the middle. Fold up the sides and then squeeze out some moisture over your sink. You’ll want enough leftover to fill the 1/2 cup.
Add flour, oats, salt, baking soda, and pumpkin pie spice to a bowl. Whisk to combine.
Add butter to large saucepan over medium heat. Butter will begin to foam and then brown quickly. Stir constantly during entire process. Once butter begins to brown, remove from heat and pour into a mixing bowl. Set aside to cool for 10 minutes. Reserve 1 & 1/2 tablespoons for the brown butter icing step later.
Mix in brown sugar and granulated sugar. Mix until combined.
Add pumpkin puree, egg yolk, and vanilla extract. Mix until combined.
Add flour mixture into the pumpkin mixture and mix until combined.
Cover the bowl and place in refrigerator for 30 minutes.
Scoop out 12 cookies using a #20 (3 tablespoon) cookie scoop. Cover and refrigerate cookies for 3 hours.
Preheat oven to 325° F. Line a baking sheet with parchment paper. Bake for 14 minutes.
Remove from the oven and let cool on baking sheet for 10 minutes before transferring to a wire rack to cool completely.