Preheat oven to 300 degrees. Line a large baking sheet with parchment paper. Spread the chopped pecans on the sheet and toast for 7-8 minutes. Remove from the oven and allow to cool for 10-15 minutes.
Turn the oven up to 350 degrees. Grease two or three 9-inch cake pans, line with parchment paper, then grease the parchment paper.
Whisk the brown sugar, granulated sugar, oil, eggs, applesauce, and vanilla together in a large bowl until combined and no brown sugar lumps remain. In another large bowl, whisk together the flour, baking powder, baking soda, salt, cinnamon, and ginger.
Pour the wet ingredients into the dry ingredients and, using a rubber spatula or wooden spoon, fold the ingredients together until just combined. Fold in the carrots and 1 cup of the toasted pecans.
Pour the batter evenly into the cake pans. If using 3 cake pans, bake for 20-24 minutes. If using two cake pans, bake for 30-35 minutes. Test the center with a toothpick. Do not over-bake. Allow the cakes to cool completely in the pans on a wire rack. The cakes must be completely cool before assembling and frosting.