Preheat the oven to 350°.
Shredding the carrots:
Using a vegetable peeler, remove the outer layer from the carrot then using the finest holes on a box grater, shred the carrots.
In a small bowl whisk the flour, baking soda, salt and cinnamon then set aside.
In a medium bowl blend by hand the vegetable oil, brown sugar, eggs, unsweetened applesauce, vanilla and grated carrots. Using a mixer will make the cupcakes dense.
Gradually fold the flour mixture into the wet mixture just until it’s combined without overmixing.
Grease a muffin tin or line with papers then divide the batter between them about 2/3 of the way up each. Bake 18-20 minutes or until toothpick inserted comes out clean then cool completely.
Using a hand mixer, combine the frosting ingredients. It's important the butter and cream cheese are room temperature.
This recipe makes a generous amount of frosting and can be halved if you prefer less. Frost each cupcake then sprinkle with finely chopped pecans.