Make the Ice Cream: Beat cream cheese until smooth with a hand mixer. Beat in sweetened condensed milk. Switch to a wooden spoon or spatula and stir in vanilla. Fold in Cool Whip. Place in a sealable container and freeze until hardened, overnight is best.
Make the Cake: Preheat oven to 350 degrees. Grease and flour two 6” round cake pans or one 9” round cake pan.
Stir together eggs, oil, applesauce, and vanilla. Stir in sugars. Add salt, baking powder, baking soda, and cinnamon and stir until they are just mixed in. Add flour and stir until smooth. Stir in pecans and carrots.
Pour batter evenly into pans (or into the one 9” pan). I used to 6” round pans, but this batter should fit into a 9” pan. Fill about 2/3 full.
Bake for 22-25 minutes until a toothpick comes out clean. (My two 6” pans baked in 24 minutes. The centers fell a little when I removed them from the oven, but that doesn’t matter. We’re covering it with ice cream!)
Cool completely before removing from pans. Wrap in plastic and freeze until ready to assemble the cake. This can be done up to a week ahead of time.
Assemble the Cake:Line the bottom of whatever size cake pan you used to bake the cake (either the 9” or one 6” pan) with plastic wrap.
Remove ice cream from freezer. If it’s too hard, let it sit for a few minutes. Scoop ice cream into the bottom of the plastic wrap lined pan and press to compact with your hands. If you are using a 6” pan you’ll use about 2/3 of the ice cream. If you’re using a 9” pan, use it all.
Take your cake layer (only one of them if they are 6”) and press it gently on top of the ice cream. Wrap the entire thing in plastic wrap and freeze for at least a few hours.
Note: I only used one of my 6” cake layers. I kept the other frozen for future cake needs.
When it’s good and frozen, remove from freezer. Unwrap and turn it out onto a serving plate. Peel off the plastic wrap gently from the ice cream.
Frost with your frosting and line the sides with chopped pecans. Serve immediately or refreeze until ready to serve.