Preheat oven to 350F. Spray a 9x13 pan with cooking spray and set aside.
Mix together the sugar, applesauce, oil and eggs in a large bowl. In the same bowl add your flour, salt,
baking powder, baking soda and spices. Stir to combine. Then add carrots and walnuts and mix to combine. Do not overmix.
Pour into your prepared pan. Bake for 35-40 minutes or until a toothpick comes out clean. Cool completely.
In a bowl of a stand mixer with a paddle attachment, cream butter and cream cheese. Add sugar and vanilla and blend . Spread on cooled carrot cake.
Notes
Be sure to measure your flour correctly by spooning into your cup and levelling with a flat edge. If you don't, you may end up with too much flour and that will result in a dense cake.
Once you have combined your wet and dry ingredients, be sure to not overmix. Once your flour becomes wet, the gluten will be formed. Too much mixing results in too much gluten formed and that results in a tough cake.
Make sure your eggs are room temperature so they will be incorporated easily. Place them in a warm bowl for 10 minutes before using them.
Grate your carrots by hand. A food processor will grate the carrots too fine and turn them into more of a mush.
Allow your cake to cool completely before frosting. If the cake is too warm, your icing will melt.