Line two baking sheets with parchment paper. Set aside.
In a medium bowl, whisk together flour, baking soda, salt, and pumpkin pie spice. Set aside.
In a large mixing bowl, beat browned butter, brown sugar, and white sugar with a hand mixer until light and fluffy. Add in the egg and vanilla extract. Mix until combined.
Slowly mix in the pumpkin puree and sourdough starter discard until fully incorporated.
Gradually add the dry ingredients to the wet mixture. Mix until just combined. If desired, fold in chocolate chips or nuts.
Cover the dough with plastic wrap and chill for 30 minutes.
While the dough chills, preheat the oven to 350°F (175°C).
Use a cookie scoop to portion the dough onto the prepared baking sheets. Bake for 12-14 minutes or until the edges are golden brown.
Let the cookies cool on the baking sheet for 5 minutes before transferring to a wire rack to cool completely.