Preheat oven to 375 degrees F.
Lay a piece of parchment paper down on the bottom of a 15x10-Inch jelly roll pan and grease the sides of the pan.
In a bowl, combine brown sugar and applesauce very well.
Add in pumpkin and combine again.
Add in flour, baking soda, baking powder, cinnamon, nutmeg, ginger, cloves, allspice, and salt. Combine, scraping down the sides if needed.
Stir in the chopped walnuts if desired.
Spread the mixture evenly across prepared baking sheet.
Place into oven for 13 to 15 minutes. The cake should spring back when touched.
Remove from oven.
Sprinkle the entire thing with powdered sugar, then place a kitchen towel over top and immediately invert the pan. Carefully peel off the parchment paper. Sprinkle this side with powdered sugar also.
Starting at the narrow end (smaller), roll up the cake and towel together (see video if needed). Place on a wire rack to cool for 1 hour. *Placing on a wire rack to cool is very important.