Preheat your oven to 300°F (149°C). Line a large baking sheet with parchment paper or a silicone baking mat. Spread out the chopped pecans and toast them for 7-8 minutes. Once done, remove from the oven and let cool for 10-15 minutes.
Increase the oven temperature to 350°F (177°C). Prepare two or three 9-inch cake pans by greasing them, lining with parchment paper rounds, and then greasing the parchment paper as well. This ensures the cakes will release easily.
In a large bowl, combine the brown sugar, granulated sugar, oil, eggs, applesauce, and vanilla extract, whisking until well-mixed and free of brown sugar lumps. In another bowl, whisk together the flour, baking powder, baking soda, salt, cinnamon, ginger, nutmeg, and cloves. Gradually add the wet ingredients to the dry, folding gently with a rubber spatula or wooden spoon until just combined. Incorporate the grated carrots and 1 cup of the toasted pecans.
Divide the batter evenly between the prepared cake pans. For three pans, bake for 20-24 minutes; for two pans, bake for 30-35 minutes. Test for doneness by inserting a toothpick into the center—if it comes out clean, the cakes are done. If not, bake a little longer, being careful not to over-bake. Allow the cakes to cool completely in the pans on a wire rack before frosting.
For the frosting, beat the softened cream cheese and butter together on medium-high speed until smooth, about 2 minutes, using a handheld or stand mixer fitted with a whisk or paddle attachment. Add the confectioners’ sugar, vanilla extract, and a pinch of salt. Start mixing on low speed for 30 seconds, then increase to high speed and beat for 3 minutes until fully combined and creamy. Adjust the consistency if needed by adding more confectioners’ sugar (if too thin) or a bit of milk (if too thick), and adjust sweetness with a pinch of salt.
To assemble, first level the tops of the cooled cakes with a large serrated knife or cake leveler. Place one layer on a cake turntable, cake stand, or serving plate, and evenly spread a layer of frosting on top. Add the second layer, more frosting, and then the third layer. Cover the top and sides of the cake with the remaining frosting, and garnish with the rest of the toasted pecans. Refrigerate the cake for at least 15-20 minutes before slicing to help it hold its shape.
Store any leftover cake tightly covered in the refrigerator for up to 5 days.