Preheat oven to 350F. Grease a muffin pan or spray paper liners to prevent sticking and set aside. In a medium bowl, mix flour, baking powder, soda, sugar, salt and cinnamon in a medium bowl. In a large bowl, mix applesauce, vanilla and carrots. Add dry mix to wet mix in 3-4 batches.
I like to add raisins and top some with chopped walnuts. I always double my muffin recipes and freeze some.