1. Preheat oven to 350 degrees.
2. In a large bowl, cream together oil, sugar and eggs. You can do this by hand or with an electric mixer.
3. Add vanilla extract, applesauce, and crated carrots, and mix well.
4. In a separate bowl, mix flour baking soda, baking powder, salt and spices. Add the dry ingredients to the batter and mix just until incorporated.
5. Pour the batter into a parchment paper lined (or greased) 9 by 9 inch baking pan and bake for 20-25 minutes or until a toothpick inserted into the center comes out clean.
6. Cool completely, and then frost and cut into bars.

For the Frosting

1. With an electric mixer, whisk softened cream cheese, vanilla extract, and salt until smooth and creamy. Gradually add powdered sugar as you mix.
2. Reserve 1 cup of frosting for the carrot decoration. Spread the remaining frosting over the cooled cake.
3. Divide the reserved frosting into two bowls and mix a few drops of green food coloring with one and orange with the other. Spoon the frosting into two bags fitted with a small tip if you have it, or cut off the corner of a zip top bag. Start by making the stems with the green frosting, and then add the carrot.