Preheat oven to 350°F. Butter two 9-inch cake pans.
In a medium bowl, sift the flour, baking soda, cinnamon, and salt. Set aside.
In another large mixing bowl, mix together the oil, applesauce, sugar, and eggs until well combined.
Slowly add in the flour mixture and continue to mix until well blended.
Fold in the shredded carrots.
Pour the cake batter evenly into the cake pans and bake 35 minutes or until the the center comes out clean when inserting a toothpick. Remove from the oven and let cool for 10 minutes before turning out.