Preheat oven to 350 degrees F. Line a baking sheet with parchment paper and set aside.
In a medium bowl, mix together the dry ingredients: all-purpose flour, ground cinnamon, salt, nutmeg and cloves.
To a large bowl, add the room temperature butter and light brown sugar. Using a stand-up mixer with the paddle attachment, cream the two together until the butter is light and fluffy, about 5 minutes. Add the egg, baking soda and persimmon pulp and mix until thoroughly combined. (You may still see a few chunks of persimmon throughout the mixture; as long as there aren't a ton, you'll be a-ok!)
In two batches, add the dry ingredients to the wet ingredients, combining in between batches. When you no longer see any traces of flour, fold in the chopped pistachios, making sure they're evenly distributed throughout the dough.
Using a 2-ounce cookie dough scooper, drop cookie dough rounds onto your cookie sheet, being sure to space them apart by about 2 inches. Flatten the cookies slightly with your fingers and transfer to the oven to bake for about 10-12 minutes. You'll know the cookies are done when the edges are lightly golden brown and the middle will be soft yet should spring back a bit. Allow to cool for a minute or so on the baking sheet and then transfer to a rack to cool.