Preheat the oven to 300 degrees and line a large baking sheet with parchment paper. Spread the chopped pecans evenly and bake for 7-8 minutes. Set aside to cool
Increase oven temperature to 350 degrees and grease 3 9-inch cake pans and line bottoms with parchment paper
In a large bowl whisk together flour, baking powder, baking soda, salt, cinnamon, ginger, nutmeg, and cloves. Set aside
In a medium bowl whisk together brown sugar, granulated sugar, oil, eggs, apple sauce, and vanilla together until combined. Keep whisking until no clumps of brown sugar are left
Pour the wet ingredients into the dry ingredients and use a spatula or wooden spoon to fold together. There should still be a bit of flour visible
Gently fold in 1 cup of the toasted pecans and shredded carrots until combined
Pour the batter evenly into each of the prepared cake pans and bake in a preheated oven for 20-24 minutes until a toothpick comes out clean when inserted into the center
Remove cake pans from oven carefully and place pans directly on a wire rack to cool completely before frosting
Begin making the frosting by beating the cream cheese and butter in a large bowl using a hand mixer. Beat on medium-high speed for about 2 minutes until smooth
Slowly add in the confectioners’ sugar, cream or milk, vanilla, and salt. Beat for another 30 seconds on low speed, then for 3 minutes on high speed until completely smooth (if the frosting is too thick, add a bit more milk, if it is too thin add a bit more sugar)
To begin assembling the cake place one layer on a plate or cake stand and evenly cover the top of the layer with frosting
Continue with the next 2 layers adding frosting in between
Cover the entire outside with frosting. Decorate with the remaining toasted pecans and refrigerate for 15-20 minutes prior to serving