Preheat oven to 350 degrees. Grease two 9x9 inch pans (or a 9x13 inch pan) In a large bowl combine flour, cinnamon, ginger, nutmeg, baking soda, baking powder and salt.
In a medium sized bowlwhisk together vegetable oil, brown sugar, white sugar, eggs, applesauce, and vanilla. Add to the dry ingredients and combine.
Fold in the carrots and chopped pecans. Divide the batter evenly into the baking dishes. Bake for 25-30 minutes or until golden brown and toothpick inserted comes out clean. Let the cakes cool.
To Make the Cream Cheese Frosting:
To make the cream cheese frosting: Beat the cream cheese and butter together until smooth add vanilla. Add in the powdered sugar one cup at a time until you get your desired consistency. Frost on cooled cakes.