Preheat oven to 350. Grease and flour 2 9-inch round cake pans.
Grate carrots on a fine grater and set aside.
In a large mixing bowl, whisk together eggs, oil, and sugar. Whisk vigorously for about a minute.
Add flour and baking soda and gently whisk until completely incorporated.
Stir in carrots.
Fold in 1 cup of cooked caramel apples into the batter.
Separate the batter among the 2 prepared baking pans. (You can weigh them on a scale to make sure that the batter is divided equally.)
Bake for 35-40 minutes.
Take the cakes out of the oven and allow them to cool for about 15 minutes.
Gently run a greased butter knife along the side of the cake pan to help separate the cake from the pan. Gently tap the cake pans on the counter to loosed the cake a bit, tip the cake pans, and take the cakes out of the pans.
Let the cakes cool completely on a wire rack.
Make sure the cakes and the apples are cooled completely before frosting.