Preheat the oven to 350 F (175 C) and spray a square baking dish with cooking spray.
In a large mixing bowl, combine the oil, sugar, brown sugar, eggs, salt, cinnamon, ginger, cloves, and baking soda. Mix until fully combined, then add in the flour, carrots, nuts, and any other add-ins you are using. Mix until just combined. Pour it into your prepared baking dish and bake for 35-40 minutes, until a toothpick inserted comes out clean (a few crumbs are fine). Allow to cool for an hour before icing.
While the cake cools, make the icing. In a mixing bowl, combine the softened cream cheese, butter, and vanilla. Using a hand mixer, beat together until combined and fluffy. Add in the confectioner's sugar and salt and beat until fully incorporated. If the icing is too loose, add a bit more sugar. If the icing is too thick, add milk or water by the teaspoon.
Once the cake is cooled, ice it. Pour the icing directly onto the cake in the pan and spread it evenly with a spatula or the back of a spoon. Top with garnish of your choice. I topped mine with more nuts.