Preheat your oven to 350°F. Line two baking sheets with parchment paper or silicone baking mats.
In a small saucepan, melt the butter over medium heat. Continue cooking, swirling the pan occasionally, until the butter starts to foam and turns a deep golden brown color with a nutty aroma. This should take about 4-6 minutes. Be careful not to burn the butter.
Once browned, immediately remove the butter from the heat and pour it into a heatproof bowl to cool slightly.
In a large mixing bowl, whisk together the cooled brown butter, pumpkin puree, brown sugar, granulated sugar, egg yolk, and vanilla extract until smooth and well combined.
In a separate bowl, whisk together the oats, flour, baking soda, baking powder, salt, cinnamon, and pumpkin pie spice.
Gradually add the dry ingredients to the wet ingredients, mixing just until combined. Be careful not to overmix.
Use a cookie scoop or spoon to portion out the dough onto the prepared baking sheets, leaving about 2 inches between each cookie.
Bake in the preheated oven for 10-12 minutes, or until the edges are lightly golden and the centers are set. The cookies may look slightly underdone in the center, but they will continue to set as they cool.
