Preheat the oven to 350 degrees F. Line a 12-cup muffin tin with paper liners or spray tins with non-stick cooking spray.
In a large bowl whisk the applesauce, maple syrup or sugar, flax egg, melted vegan butter or oil, and vanilla. Stir in the flour, baking powder,, cinnamon, and salt. Stir ingredients together until just combined and flour still showing through.
Fold in the shredded carrots and any of your add-ins and mix until just combined without overmixing. Overmixing makes them chewy.
Using an ice cream scooper, divide the batter between the prepared muffin cups and bake 15-20 minutes, or until a toothpick inserted in the center of a muffin comes out clean. Remove muffins from tins shortly after baked and transfer to a wire rack to cool.
If you want to add vanilla glaze for a sweeter treat, mix together 1 cup of powdered sugar and 1-2 tablespoons almond milk and drizzle over muffins.
To store, seal at room temperature for up to 3 days.