Start by baking the cakes.
Preheat your oven to 350F. Spray your cake pans with baking spray and set aside.
In the bowl of a stand mixer, combine your wet ingredients: the sugar, melted butter, eggs, vanilla, applesauce, and grated carrots.
In another bowl off to the side, whisk together your dry ingredients: the flour, baking soda, salt, cinnamon, nutmeg, ginger. Add in thirds to your wet ingredients and mix to *just barely combine*.
Add in the nuts in last and fold to combine, if you wish.
Divide the batter evenly among the 3 pans -- it'll be about 21 ounces of batter per cake pan.
Bake for about 30 minutes, until the sides of the cake are pulling away from the cake pan.
When done, let them cool in their pans for about 5-10 minutes. Then, flip them onto a cooling rack, and stick in your freezer while you make the frosting.
Make the cream cheese frosting next.
In the bowl of a stand mixer fitted with the paddle attachment, beat the cream cheese, butter, vanilla, and the pinch salt on medium-high speed until light and fluffy.
On low speed, add in the powdered sugar in thirds, until nicely combined. Scrape down the sides to make sure everything's incorporated.
It should be very pliant and well-combined.
Assemble the cake
Pull the cake layers out of the freezer, and place a dab of frosting on a plate or a cake platter (this helps 'glue' the cake down to the platter), and place the cake layer upside down (so the flattest part is face-up). Spoon about 1/4 of your frosting on that layer, and spread around evenly using an offset spatula.
Repeat with the next two layers. You'll have a naked cake after you've applied frosting to the 3 layers on each one's top only.
Stick the cake in the fridge for about 10 minutes to let the frosting firm up before doing the sides.
Come back to the cake and apply the rest of your frosting on the sides. I use my offset spatula and apply globs of frosting on the sides, then smooth it around/try to get it to be uniformly applied. Once there's an even amount of frosting, using a bench scraper, place the bench scraper perpendicular to the cake and gently drag it around the cake, to even out the sides. Here's a video that shows that in more detail.
Serve immediately, or store in the fridge until you're ready -- it will last about 3-4 days in the fridge.