First, preheat oven to 325 degrees Fahrenheit. Next grease and flour two 9-inch round cake pans. If desired add parchment circles to the bottom of the pans for easy cake removal.
In a large bowl mixing bowl, mix together flour, sugar, baking soda, cinnamon and salt.
Using a separate bowl, beat eggs slightly. Add oil and vanilla extract to eggs. Stir to combine. Add shredded carrots and apple sauce to the mixture and stir to combine.
Fold the wet mixture to dry mixture and stir until just combined. Do not over stir.
Finally spoon batter into prepared pans and bake for 40 to 45 minutes or until a toothpick inserted into the center of the cakes comes out clean.
Cool cake for approximately 10 minutes in pans, then transfer cake to wire racks to cool completely prior to frosting.