Preheat the oven to 400 degrees Fahrenheit. Coat a 12 cup muffin tin with cooking spray (or use paper or silicone liners*)
In a medium mixing bowl, whisk together flour, baking soda, baking powder, pumpkin pie spice, and salt. Add to wet mixture and stir until just combined.
In a separate larger bowl, whisk together eggs, sugar, pumpkin puree, applesauce, vanilla, and oil in a bowl.
Fold in 1/2 cup of shredded carrot and 1 cup of mini chocolate chips.
Spoon the batter evenly across the 12 muffin cups and sprinkle a few additional chocolate chips on top of the muffins as desired.
Bake for 18-20 minutes, or until lightly browned and a toothpick inserted in the center of a muffin comes out clean. (Check at 15 minutes if not using the silicone liners).
Cool for 5 minutes in the pan, then transfer the muffins to a plate or wire rack to cool completely.
Serve (I recommend at least testing one while the chips are still warm), or store the muffins in an airtight container for up to 5 days.