In a mixing bowl, beat together brown sugar, maple syrup, nut milk, applesauce, vanilla extract, and eggs. Your batter is going to be very wet.
Using a cheese grater or food processor, shred carrots. Fold shredded carrots into the batter with a rubber spatula or mixing spoon.
Next, add the rest of the dry ingredients. Beat until thoroughly mixed. Pour batter into the pan and sprinkle with pecans.
Bake for 30 minutes or until a toothpick inserted in the center comes out clean.
While the bars are baking, gather frosting ingredients in a mixing bowl. Then, using a hand mixer, beat everything together. Set aside.
Remove bars from the oven when cooked and let cool for 10-15 minutes. Top with icing and serve!