Cream the melted butter, brown sugar, and white sugar together in a medium mixing bowl on medium speed until fluffy and no brown sugar lumps remain. Add the pumpkin puree, vanilla extract, and sourdough discard and mix until well combined (scrap the sides of the bowl to ensure everything is mixed properly). Set aside.
In a small bowl, whisk together the all-purpose flour, salt, baking soda, cinnamon, and pumpkin pie spice.
Add the dry ingredients to the wet ingredients and mix until combined, but not overmixed. The dough will be quite soft. If adding white chocolate chips or nuts, add at this point. (Note: they may be hard to combine with the dough due to the melted butter. Just do your best!)
Cover the bowl with plastic wrap or a lid and chill for 30 minutes or up to three days if you want to long ferment the dough.
When ready to bake, preheat the oven to 350 degrees Fahrenheit, and line a baking sheet with parchment paper. In a small bowl, combine the white sugar and cinnamon to make the cinnamon sugar coating.
Using a cookie scoop or spoon, scoop two tablespoons of dough and roll into a ball. Dip each ball into the cinnamon sugar mixture and roll to evenly coat. Place the cookie dough balls on the prepared baking sheet about 2 inches apart. Use your fingers to press each cookie dough ball out slightly.
Bake for 10-13 minutes, or until the edges are set and lightly golden and the center is still soft. Remove from the oven.
Allow them to cool on the baking sheet for 10 minutes, and then remove to a wire rack and allow to cool to room temperature.
Store in an airtight container.