Preheat oven to 350 degrees and line to 8 inch round cake pans with parchment (cut out a circle of parchment slightly smaller than the size of the cake pan and place in the bottom of each cake pan). Spray pans with cooking spray.

Mix together dry ingredients in a medium bowl.

Use a cheese grater or a food processor with the shredding attachment to shred up the carrots.

In a stand mixer, combine the oil (and apple sauce if using) with the brown sugar. Add in the eggs one at a time. Then add in the vanilla. Add the dry mix in two separate additions. Stir in the carrots and optional walnuts.

Pour batter into prepared cake pans.

Bake for 35-40 minutes or until cake bounces back when you gently press into it with your finger tip.

Let cool in pans for 10 minutes or so, then, use a knife to loosen up the edges of each cake around the pan. Carefully turn out cakes onto a wire drying rack.

Prepare frosting:

Melt butter over medium heat then add in the brown sugar, cream, and salt. Stir over medium heat until sugar dissolves (about 3-4 minutes). Transfer warm caramel to a stand mixer (or you can use a medium bowl and a hand mixer) and add in the powdered sugar. Whip the frosting until well combined (smooth without any lumps of powdered sugar). Add a tablespoon or so of more cream if the frosting is too thick. Use frosting while its still warm to frost the cake.

Place one layer of the cake on a cake stand and spread out 1/3 of the frosting on the first layer. Add the second layer of cake then top with remaining frosting, letting the warm caramel frosting drip over the edges. As the frosting cools it will harden.