Preheat oven to 350 degrees Fahrenheit and grease a half-sized sheet pan (18"x13").
In the bowl of an electric mixer, cream together granulated sugar, brown sugar, eggs, vegetable oil, applesauce and shredded carrots.
In a separate bowl, stir together flour, baking powder, baking soda, cinnamon, nutmeg, cloves and salt. Add it to the wet mixture and mix until combined, scraping down the sides and bottom of the bowl with a rubber spatula in between.
Pour and spread batter evenly into prepared half sheet pan. Bake for approximately 17-20 minutes, or just until a toothpick inserted into the center comes out mostly clean. Moist crumbs are ok. Be careful not to overbake.
Allow the cake to cool completely. Then make the frosting by creaming together cream cheese, butter, powdered sugar and vanilla until smooth and creamy and no lumps remain. Spread over cooled cake, then top with chopped pecans. Slice and serve.