Stir together the dry ingredients and set aside. In a saucepan, stir together the water, butter, pumpkin puree, dark brown sugar and salt. When the butter melts, stir in the dry ingredients.
Beat in an egg, one at a time. Scrap down the side of the bowl as necessary to ensure everything incorporates.
Cut parchment paper into small squares. Pipe the dough onto each square. Drop into oil to fry. Remove the paper with metal tongs.