Preheat the oven to 300°F. Line a baking sheet with parchment paper and spread out the pecans in an even layer and bake for 7-8 minutes, just to toast them. Remove from the oven and allow to cool.
Increase oven temp to 350°F. Grease two 9" cake pans and line the bottom with parchment paper, and then grease the parchment paper as well. If you only have one cake pan (like me!) divide the recipe in half and reuse the same cake pan.
In a medium bowl, whisk together the sugars, oil, eggs, vanilla, and applesauce until smooth, and set aside. In a large bowl, sift the flour, baking powder, baking soda, salt, cinnamon, ginger, nutmeg, and cloves, and then whisk together until well combined. Pour the wet ingredients from the first bowl into the dry ingredients, and fold together with a rubber spatula just until fully combined. Fold on the shredded carrots and 1 cup of toasted pecans.
Pour the batter into the prepared cake pan/s and bake for 30-35 minutes. The cake is done when a toothpick comes out clean. Once baked, allow the cakes to cool completely *in the pan* on a wire rack before attempting to take them out of the pans. This will take some time, and can even be done the day before (once cooled, the cakes can be wrapped tightly in plastic wrap and stored in the fridge overnight, and assembled the next day).
When the cakes have cooled and you are ready to assemble your cake, make the frosting. In the bowl of a stand mixer, cream the butter and the cream cheese together on medium-high speed until smooth. Add the powdered sugar, cream, vanilla, and a pinch of salt. Start the mixer on low speed first, or else half the powdered sugar will end up on your counter, and then speed up to high speed and mix until completely smooth. Scrape down the sides with a rubber spatula as necessary. If the frosting isn't quite the consistency you want, you can adjust the ingredients here, adding more powdered sugar if it's too thin and runny, and more milk if it's too thick. You want it soft and spreadable, but it should still be firm enough to not run on the cake.
To assemble the cake, first take a sharp serrated knife and cut the top of the cakes level. Place one of the cake halves bottom side down on your cake stand (or whatever you plan to serve the cake on). Optionally you can place some frosting down on the cake stand first to help the cake stick. Evenly cover the top of the cake with frosting; make sure it's not too thin here or it won't show very well when you cut a slice. Next place the second layer cut side down, so the bottom of the second piece is facing up. This helps ensure that you have a very flat and clean top for your cake. Cover the top and sides with the remainder of the frosting to your liking, I had plenty of frosting left over so don't feel the need to use it all (but also it's delicious so I get it if you choose to!). Garnish the top of the cake with the remaining chopped pecans.
I recommend refrigerating the cake for at least 20 minutes before cutting.
Enjoy!
