Preheat the oven to 350°F/175°C and line and grease a 9×9 inch square pan. Grate the carrots using the fine side of your grater.
In a medium-sized bowl, add in flour, baking soda, baking powder, cornstarch, cinnamon, nutmeg, cloves, ginger, and salt. Mix together and set aside.
2 cups all-purpose flour, 1 tbsp cornstarch, 1 tsp baking soda, 1 tsp baking powder, 2 tsp cinnamon, 1/8 tsp nutmeg, 1/8 tsp cloves, 1/8 tsp ginger
In a large bowl, add brown sugar, eggs, and vanilla. Whisk this for 2-3 minutes until well combined.
1 cup light brown sugar, 3 eggs, 1 tsp vanilla
Whisk in the oil, and then the applesauce, and then the grated carrots.
1/3 cup unsweetened applesauce*, 2/3 cups oil, 2 cups carrots
Toss in the dry ingredients and using a spatula, mix until just combined and no dry streaks appear.
Transfer into the prepared pan and spread evenly. Bake for 30-40 minutes or until a toothpick inserted in the middle comes out clean (mine took 35 minutes exactly).
Once the cake is cooled, make the glaze by mixing together sour cream and powdered sugar. Spread evenly on the cake and sprinkle chopped pecans.
1 cup powdered sugar, 2-3 tbsp sour cream*, 1/4 cup pecans
Allow to cool, slice, and enjoy!