Preheat the oven to 350°F (176˚C) and grease and flour two 8 inch cake pans, or line them with parchment paper to prevent sticking.
Shred the carrots in a food processor or with a box grater. Set aside
Chop the pecans with a food processor or a knife. Set aside. (You can purchase chopped nuts but they’re generally more expensive than whole nuts.)
In a medium mixing bowl, whisk the 3 cups flour, 1 tsp baking powder, 1 tsp baking soda, 2 tsp ground cinnamon, 1 tsp ground nutmeg, ½ tsp ground allspice, ½ tsp ground ginger, and ½ tsp salt until combined.
In a large mixing bowl mix the 1 cup applesauce, ¾ cup coconut sugar, and 1 tsp vanilla extract on medium high until light and fluffy. Approximately one minute.
On a low speed add one quarter of the dry ingredients to the applesauce mixture and blend until just combined. Add one quarter of the buttermilk while blending the flour into the sugar. Continue adding one quarter of flour and one quarter of the buttermilk until all of the flour mixture and milk is combined. Don’t over beat the mixture or the batter will become tough.
When the dry and wet ingredients are just blended, remove the mixing bowl from the mixer and scrape the batter off of the mixing paddle into the bowl, then fold the carrots, pecans, and raisins into the mixture until evenly combined.
Pour half of the batter into one cake pan and the other half into the second cake pan.
Tap the pans on a hard surface a few times to remove air bubbles and bake for 30 to 40 minutes or until the tops are firm and slightly cracked and a toothpick comes out clean. Check them at 25 minutes as some ovens bake faster than others.
Cool in the pans for 5 minutes and then invert them onto a wire rack and let them cool completely before frosting.