Preheat the oven and prepare the pans. Preheat the oven to 350 F. Prepare three 8" cake pans. Add a parchment round to the bottom of each pan and grease the parchment paper and the pans.
Mix the wet ingredients and sugar. In a large mixing bowl, beat the brown sugar, granulated sugar, oil, eggs, apple sauce, and vanilla together.
Sift the dry ingredients. In the second large mixing bowl, sift together all-purpose flour, cinnamon, nutmeg, ginger, baking soda, baking powder, salt, and whisk.
If using pecans, in a separate bowl coat the pecans with 2 tablespoons of the dry ingredients.
Add the dry ingredients to the wet ingredients. Mix together until just combined and scrape the bowl down.
Fold the carrots and pecans into the batter.
Divide the batter evenly into three-lined and buttered 8" pans
Bake for about 40 minutes, or until a toothpick comes out clean. Leave the cakes in the pans for about 5-10 minutes before removing them from the pan onto a wire rack to cool.
Make the cream cheese frosting. Cream the butter and cream cheese in the bowl of an electric mixer with the paddle attachment on medium speed. Whip until light and airy around 3-4 minutes.
While the mixer is on low, pour in the vanilla and slowly add the powdered sugar and mix until smooth. (For a more stabilized easily spreadable frosting, simply add more powdered sugar until you reach your desired consistency.)
Make buttercream frosting carrots. In a mixing bowl, whisk up the butter until light and creamy. Then use a spatula and fold in the powdered sugar until it forms a thick pipeable consistency. Divide into two bowls and use food coloring to dye one bowl green and one bowl orange. Make sure to add more buttercream to the orange bowl.
Assemble the cake. Pipe a thick layer of the cream cheese frosting onto the first cooled cake layer, add the second layer then repeat the process until the cake is built. Cover the cake in cream cheese frosting then smooth the side and top.
Decorate the cake. Using a small round piping tip, pipe the carrots and the stems and add in the touch of pecans around the bottom layer. You can decorate the cake however which way you choose. This is the fun part! Go nuts!