Preheat the oven to 300°F (149°C). Line a baking sheet with parchment paper.
Toast the pecans: Spread the chopped pecans on the prepared baking sheet and toast for 7-8 minutes, or until fragrant and lightly browned. Remove from the oven and set aside to cool.
Grease and line the cake pans: Grease two or three 9-inch cake pans with butter or nonstick cooking spray. Line the pans with parchment paper circles.
Whisk the wet ingredients: In a large bowl, whisk together the brown sugar, granulated sugar, oil, eggs, applesauce, and vanilla extract until well combined.
Whisk the dry ingredients: In a separate large bowl, whisk together the flour, baking powder, baking soda, salt, cinnamon, ginger, nutmeg, and cloves.
Combine the wet and dry ingredients: Add the wet ingredients to the dry ingredients and stir until just combined. Do not overmix.
Fold in the carrots and pecans: Fold in the grated carrots and 1 cup of the toasted pecans.
Divide the batter: Divide the batter evenly among the prepared cake pans.
Bake the cakes: Bake for 20-24 minutes if using three cake pans, or 30-35 minutes if using two cake pans. A toothpick inserted into the center of a cake should come out clean when done.
Cool the cakes: Let the cakes cool completely in the pans on a wire rack before frosting.
Make the frosting: In a large bowl, beat together the cream cheese and butter until light and fluffy. Beat in the confectioners' sugar, vanilla extract, and salt until smooth and creamy.
Frost the cake: Place one cake layer on a serving plate or cake stand. Spread a generous layer of frosting over the top. Repeat with the remaining cake layers. Frost the top and sides of the cake with the remaining frosting.
Garnish with pecans: Garnish the sides and top of the cake with the remaining toasted pecans.
Refrigerate the cake: Refrigerate the cake for at least 15-20 minutes before slicing. This will help the cake set and make it easier to slice.