Preheat the oven to 350F. Grease and flour an 8x8 inch square baking pan. (Note: I normally serve this cake from the pan, but if you would like to un-mold it, line the pan with parchment with overhang instead, for easy removal)
In a medium bowl, whisk together the flour, baking powder, baking soda, salt, and cinnamon.
In a large bowl, whisk together the brown sugar, oil, applesauce, pumpkin puree, eggs, and vanilla.
Add the dry ingredients to the wet ingredients and stir until just combined.
Fold in ¼ cup of the chocolate chips. Pour the batter into the prepared baking pan and sprinkle the top with the remaining chocolate chips.
Transfer to the preheated oven and bake for 35-40 minutes until a toothpick inserted in the center comes out clean.
Transfer the pan to a wire rack and let it cool completely before serving. OR, if you have lined the pan with parchment and plan to remove it from the pan, let it cool for 15 minutes in the pan before using the parchment overhang to lift it out of the pan and transfer to a cooling rack.