Melt butter in a small saucepan over medium-low heat. Cook, stirring occasionally, until butter starts to foam and turn brown, about 10 minutes. Immediately pour into a heatproof bowl; cover and chill until solidified, about 1 hour.

Preheat the oven to 350°F (180°C). Line four large baking sheets with parchment paper.

In a large bowl, whisk together the flour, pumpkin pie spice, cinnamon, ground ginger, baking soda, and salt. Set aside

In the bowl of a stand mixer fitted with the paddle attachment, or in a large mixing bowl using an electric mixer, cream together the browned butter, brown sugar, and granulated sugar for 1-2 minutes until well combined. Add the eggs and vanilla extract and mix until fully combined. Then mix in the pumpkin puree until well combined.

Slowly mix in the dry ingredients, making sure to stop and scrape down the sides of the bowl as needed. Then mix in the old-fashioned rolled oats until just combined.

Using a 1.5 tablespoon cookie scoop, scoop the cookie dough and drop onto the prepared baking sheets. Roll the cookie dough into balls and very gently press down with your hand to flatten each ball of cookie dough slightly. Make sure to leave a little room between each ball of cookie dough as they will spread a little while they bake.

Bake in separate batches at 350°F for 9-12 minutes or until the edges of the cookies are lightly browned and the top is set. Remove from the oven and cool on the baking sheet for 5 minutes, then transfer the cookies to a wire rack to finish cooling.