If using the pecans, preheat oven to 300°. Line a large baking sheet with parchment paper or silicone baking mat. Spread the chopped pecans on the sheet and toast for 7-8 minutes.
Remove from oven and allow pecans to cool for 10-15 minutes.
For the cake, preheat oven to 350°. 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 mixing bowl until combined and no brown sugar lumps remain.
In another large bowl, whisk the flour, baking powder, baking soda, salt and spices together.
Pour the wet ingredients into the dry ingredients. Using a rubber spatula or wooden spoon, fold the ingredients together until just combined.
Fold in the carrots and 1 cup of the roasted pecans.
Pour batter evenly into the prepared cake pans.
If using 3 cake pans bake for 20-24 minutes. If using 2 cake pans, bake for 30-35 minutes.
Test the center with toothpick. If it comes out clean, the cakes are done. Do not overbake.
Allow the cake to cool completely in the pans on a wire rack. The cakes must be completely cool before frosting or assembling.
Frost and sprinkle the remaining pecans on top.
Refrigerate for at least 20 minutes before slicing.
Chef's notes: Instead of applesauce, you may use ¾ cup crushed pineapple (slightly drained, consistency should match applesauce), ¾ cup mashed bananas, sour cream, plain yogurt, or canned pumpkin puree. Use fresh carrots, do not use packaged pre-grated carrots because they are hard and dry. You can use a 9x13 inch pan and bake for 40-45 minutes. If you would like to add in raisins or shredded coconut, reduce pecans to ½ cup. If using pineapple, soak the raisins in the pineapple juice. Keep add-ins to 1-1½ cup total (nuts, raisins, coconut, etc.). Can be stored in refrigerator, wrapped tightly, up to 5 days.