Preheat oven to 350°F (175°C). Grease or line a mini or regular muffin tin.
In a large bowl, whisk together the pumpkin, applesauce, eggs, oil, vanilla, and maple syrup.
Stir in the grated carrot.
Add the AP flour, baking powder, baking soda, and cinnamon. Mix until just combined.
Fill muffin cups to the top.
Bake: Mini muffins: 15–18 minutes/Regular muffins: 20–24 minutes
Use a toothpick to test for doneness.
Let cool completely before serving or storing.