Preheat the oven to 350°F. Spray a baking pan (size of your choice) with nonstick cooking spray.

In the bowl of an electric mixer, combine carrots, carrot purée, sugar, flour, cinnamon, baking powder, and baking soda. Mix well. Add oil, applesauce, salt, eggs, and vanilla. Continue mixing well.

Pour batter into prepared pan and bake for 40 to 45 minutes, until a toothpick comes out clean. For smaller sizes, bake for 25 minutes.

Remove from oven to cool.

In the bowl of an electric mixer, combine cream cheese, oil, confectioner’s sugar, vanilla, and lemon juice.

Frost cake only when it has cooled completely.