Preheat the oven to 400 degrees Fahrenheit.
Lightly grease a 9inch square pan (non stick spray or butter works).
Sift together your flour, cornmeal, baking powder, cinnamon, and nutmeg into a large bowl.
In a medium sized bowl, beat your eggs.
Add the pumpkin, brown sugar, and applesauce to the eggs, and whisk them all together.,
Make a hole in the middle of the flour mixture, and add in the egg and pumpkin mixture. Gently mix them together until they are just combined, but don't overmix.
Pour the batter into the prepared pan, and bake for 25-30 minutes, or until a toothpick inserted comes out clean.
Serve warm with butter, honey, molasses, etc.