On a double layer of paper towels, spread the pumpkin puree in a thin layer and let it sit for 10 minutes. Carefully blot the top with another paper towel. Using a silicone spatula, carefully scrape the pumpkin off of the paper towels. You should have at least ¼ cup (65g) of pumpkin puree.
In a medium bowl, whisk to combine the flour, baking powder, baking soda, cinnamon, pumpkin pie spice, and salt.
In a large mixing bowl, whisk to combine the melted butter and light brown and granulated sugars. Add the vanilla and the pumpkin puree, and whisk well to combine.
Add the flour mixture to the butter mixture and stir with a silicone spatula until no dry streaks of flour remain. Add most of the chocolate chips, reserving a small handful, and fold them in to distribute. (I like to reserve a handful to place on top of each cookie at the very end, but that's optional.) Cover and refrigerate the dough for 30 minutes to 1 hour.
Preheat the oven to 350°F. Use a 1½ tablespoon-sized spring-loaded cookie scoop to form 1½-inch balls (about 38g each). Then roll each into a neat ball with the palms of your hands.
Place the balls about two inches apart on two parchment paper-lined baking sheets. For less puffy cookies, you can flatten the cookies slightly to be about ½ to ¾-inch thick. (This will help them spread a bit more, but it is optional.) Place 3 to 4 of the reserved chips on top of each of the cookies.
Bake for 11 to 13 minutes or until the cookies are puffed and the edges are set. (The tops will still look slightly wet but will continue to set as they cool). Let them cool on the sheet tray for 5 minutes, then transfer to a wire rack to cool completely.