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Start by pre-heating the oven to 350 degrees F. Grab 2 9-inch round pans and generously spray with cooking spray and dust generously with flour. (Take your time preparing the pans so the cake doesn't stick) Set aside.
In a large bowl, sift together (don't skip the sifting!!) all of the dry ingredients starting with the flour (important to spoon and measure the flour so you don't end up with too much), baking soda, salt, cinnamon, nutmeg, ginger, and cloves. Whisk together and set aside.
Grab another large bowl and mix the oil, applesauce, brown sugar, white sugar, and vanilla with a large whisk until completely combined. Add in the eggs, 1 at a time, mixing after each addition.
Peel and then grate the carrots on the small side of a grater to get very fine pieces of carrots. Shred the carrots carefully. Measure to ensure you have 3 cups. Stir into the wet ingredients.
Add the dry ingredients in 3 parts to the wet ingredients mixing after each addition until they are *just* incorporated (do not over-mix to avoid a denser/tougher cake.)
Separate the mixture evenly among the prepared pans and bake for 27-35 minutes or until a toothpick, when inserted into the center, comes out clean. Remove and allow to cool for 5-7 minutes before inverting the cakes onto a cooling rack for them to finish cooling.
Meanwhile, prepare the pecans. Lower the oven temperature to 250 degrees F and line a large sheet pan with parchment paper or a silpat liner.
In a mixing bowl, whip together the egg whites, water, and vanilla until frothy. In a separate bowl, mix together sugar, salt, and cinnamon.
Add pecans to egg whites, stir to coat the nuts evenly. Remove the nuts, and toss them in the sugar mixture until coated. Spread the nuts out on the prepared baking sheet.
Bake for 45 minutes to 1 hour, stirring and tossing every 15 minutes. Remove the nuts and spread them on a sheet of parchment paper. Allow them to cool completely and harden and then finely chop the candied pecans.
Meanwhile, prepare the frosting. In a large bowl fitted to a stand mixer, add in the cream cheese and butter. Make sure both are at room temperature and not at all melted or softened.
Beat the two until completely smooth. Add in the vanilla extract and a generous pinch of salt (if desired). Beat until smooth.
Add in the powdered sugar, 1 cup at a time until you've added 3 and 1/2 cups. Remove 1/4 of the frosting now to go into the center of the cake. Add the remaining 1/2 to 1 and 1/2 cups of frosting until you have a good frosting consistency. If needed add in the heavy cream. The frosting won't be as firm as a buttercream, but firm enough to frost the cake.
To decorate: place a little frosting on the bottom of a cake pan (just to hold the bottom cake in place) and top with 1 completely cooled cake. Add the reserved 1/4 of the frosting into the center and smooth it.
Top the frosting with the other cake.
Use the remaining frosting to generously frost the cake. If the frosting is too soft, either refrigerated it or add an additional 1/2 cup powdered sugar. (You will likely have a bit of extra frosting, so don't feel like you need to use it all on the cake).
Once the cake is frosted, decorate the sides with the chopped candied pecans. Add a few to the top if desired.