Preheat the oven to 350 degrees. Lightly grease an 8X8- or 9X9-inch square baking pan (I prefer metal; if using glass, decrease oven temperature to 325 degrees).
In a large bowl, whisk together the pumpkin, granulated sugar, brown sugar, applesauce and eggs until well combined.
Add the flour, cinnamon, baking powder, ginger, nutmeg, baking soda, salt, allspice (or cloves), and chocolate chips. Stir until no dry streaks remain (don't overmix or the cake may be tough and dry instead of soft and moist).
Spread the batter evenly in the prepared pan. Bake for 25-30 minutes (40-45 minutes for a glass pan) until a toothpick inserted in the center comes out clean and the top of the batter springs back lightly to the touch.
Let the cake cool before cutting into squares.
Notes
Flour: You can sub in all-purpose flour if you don't have whole wheat flour. I prefer using white whole wheat flour. It is lighter in texture and flavor than red whole wheat flour, but either can be used.Spices: You can sub in a heaping 1 tablespoon pumpkin pie spice in place of the cinnamon, ginger, nutmeg, and allspice (or cloves).