Brown the butter by adding 1 cup of butter to a medium skillet on medium heat. Watch carefully, stirring frequently just until the butter turns an amber color. Then, promptly remove the skillet from the heat.
Pour the butter into a glass measuring cup and place in the fridge to cool for 15-20 minutes. To speed up the cooling process, place the glass measuring cup over a bowl of ice, cooling just until the butter reaches room temperature.
Preheat the oven to 350 degrees F., then line a baking sheet with parchment paper and set aside.
Add the brown sugar to a medium bowl. Then, pour in the brown butter and stir to combine.
Add egg yolk, maple syrup, vanilla and pumpkin puree to the bowl. Stir well until fully combined.
Add the remaining dry ingredients, mixing well to incorporate.
In a small bowl, stir together brown sugar, sugar and pumpkin pie spice.
Use a 2 oz cookie scoop to scoop out the dough. Then, use clean hands to roll into a ball. Place the dough ball into the sugar and spice mixture, rolling until fully coated.
Place coated dough balls onto the prepared baking sheet. Then, use your hand or the bottom of a measuring cup to slightly flatten each dough ball.
Bake in preheated oven for 12-15 minutes. Leave cookies on baking sheet for 5 additional minutes before transferring them with a spatula to a cooling rack to finish the cooling process.