Weigh or measure the granulated and light brown sugars into a small bowl, set aside. In another bowl, weigh or measure the flour, baking powder, baking soda, cinnamon, nutmeg, allspice, salt, and run a whisk through to blend.
Cube the butter into a mixer bowl and on a medium mixer speed cream the butter until it has soft looking peaks (about a minute). Add the sugars and mix for 3 minutes on a medium mixer speed. Scrape down the sides of the bowl and mix for another 30 seconds.
Next, add the egg, vanilla bean paste, pumpkin puree, and applesauce, and mix until combined. You will see colored specks running through the whole mixture. Those are just tiny specks of apple from the applesauce. Once the flour is added, everything blends together smoothly.
Scrape down the sides of the bowl and, at a low speed, add the dry ingredients about a third at a time. I take a spatula and scrape the sides and across the bottom of the bowl to make sure the flour has been incorporated. Finally, add the chopped walnuts and mix for about 15 seconds. Once combined, cover and refrigerate for an hour.
Preheat the oven to 375°F (190°C) Line 2 sheet pans with parchment paper. Grab a medium cookie scooper and you are all set.
I like using the cookie scooper since it will make the balls for me. Add a ball of cookie dough to the bowl with the powdered sugar and coat the ball. Then place on the cookie sheet pan. You can fit 12 balls on a half-sheet pan. Bake for 11-13 minutes. Move to a cooling rack once out of the oven.