Preheat the oven to 350 degrees. Grease a 12-cup muffin tin. In a medium bowl, whisk together the flour, cinnamon, baking powder and baking soda. Fold in the grated carrots. In a small bowl, whisk together the applesauce, maple syrup, eggs, melted butter and vanilla extract. Add to the dry ingredients, stirring just enough to combine. Do not overmix! Spoon into the muffin tin and bake until a toothpick comes out clean, about 18 – 20 minutes.