Preheat the oven to 350 degrees. Line the bottom of three 6-inch cake pans with parchment paper, then coat the bottom and sides of each pan with non-stick cooking spray.
In a medium bowl, whisk together the flour, salt, cinnamon, nutmeg, and cloves.
In a large bowl, whisk together the eggs and sugars until well combined. Whisk in the vegetable oil and vanilla extract until well combined.
Whisk the flour mixture into the wet mixture until just combined- do not over-mix.
Place your grated carrots in a strainer or a plate lined with a paper towel and squeeze out as much of the excess water out of the carrots as you can. Use a spatula to fold the carrots into your cake batter until just combined- do not over-mix.
Pour 1/3 of the batter into each cake pan and jiggle each pan flat on the counter to even out the batter and get rid of any air bubbles.
Bake each cake individually for 25 to 30 minutes, until the cakes are set and a toothpick comes out of the center clean. Let the cakes cool in the pan for 30 minutes before transferring to a cooling rack to cool completely.
Meanwhile, prepare the cream cheese frosting. Beat together the butter and cream cheese until smooth. Add the vanilla, salt, and one cup of confectioners sugar at a time and beat until smooth and creamy. Let it set slightly in the refrigerator while the cakes are cooling.
Once the cakes have cooled, use a cake leveler or a long cake knife to trim off the dome of each cake so that you have three flat surfaces.
Now it’s time to frost and layer! For cakes, I like to do a crumb coat of frosting first. This means that you spread about 1/4 cup of frosting on top of each cake set the crumbs and keep them from spreading around while you frost. Cover the top completely and scrape off any excess frosting so that you have a very thin layer of icing. Let that frosting layer on the cakes set in the refrigerator for 30 minutes.
Once they have set, you can spread a heaping 1/2 cup on top of each cake, then layer them on top of each other. You can either reserve some of the frosting to frost around the sides as well, or keep all of the frosting on top of each cake.
If desired, you can top the cake with royal icing and/or nuts. To toast the nuts, simply lay them out on a baking sheet and toast them in the oven at 300 degrees for 5 to 7 minutes, keeping a close eye on them to make sure they don’t burn. To layer them around the cake, simply place some nuts into the palm of your hand and gently press them into the frosting. Some nuts will slip down onto the cake stand, and that’s okay!