Preheat the oven to 350˚F with a rack in the center of the oven. Butter a round cake pan, line the bottoms with a ring of parchment paper and lightly butter the parchment. Set aside.
In a large mixing bowl, add flour, sugar, baking soda, baking powder, cinnamon, nutmeg, allspice, cloves and salt. Whisk to combine and break up any sugar clumps.
In a second mixing bowl, whisk together the wet ingredients: oil, eggs and applesauce just until well combined. Add the wet ingredients to the dry ingredients and use a spatula to fold until combined.
Use a spatula to fold in the carrot and nuts and fold until well incorporated.
Pour the batter into the prepared pan and bake in a fully preheated oven for 30-35minutes or until a toothpick inserted into the center comes out clean.
Let the cake rest in the pan for 15-20 minutes then transfer to a wire rack and cool to room temperature before applying frosting and decorating. Meanwhile, make the Cream Cheese Frosting.
Place butter into a large mixing bowl. With an electric mixer, beat butter until smooth and creamy then beat on high speed 1 minute until lightened in color.
Beat in softened cream cheese, just until combined, scraping down the bowl.Beat in vanilla and salt until incorporated. Add powdered sugar 1 cup at a time and mix on low speed until incorporated. Once all the powdered sugar is in, Increase to high speed and beat another 2-3minutes until whipped, thick and spreadable, scraping down the bowl a couple of times to ensure everything is really well blended.
Cut the Cake lengthwise into two parts.
Set the first cake layer on a cake platter and spread on a generous amount of Cream Cheese frosting (about 1/4 of the batch).
Set the second layer over the frosting with the top-side-down to create an even frosting surface. Lightly crumb coat the cake with frosting then apply more frosting to the top and sides of the cake.
Sprinkle remaining walnuts around the edges.*To improve the flavor of walnuts, toast them on a dry skillet, tossing frequently until fragrant then cool and chop.You can also substitute walnuts with pecans.