Preheat the oven to 350 degrees F. Spray two 8-inch cake pans with cooking spray and line the bottoms with parchment paper cut into circles.
In a large mixing bowl. combine flour, brown sugar, baking powder, baking soda, cinnamon, ginger, and nutmeg. Stir together to combine.
In a separate bowl, whisk together shredded carrots, applesauce, avocado oil, apple cider vinegar, and vanilla extract.
Pour wet ingredients to dry ingredients and mix until just combined and a thick batter is formed. Add in chopped nuts or raisins, if using. The mixture may seem a bit dry. Let it sit for 10 minutes so the carrots can release more moisture. Stir together one more time.
Divide the batter between the prepared pans, and bake for 25-30 minutes or until a toothpick inserted in the center comes out clean.
Cool for 5 minutes then remove from the pans and transfer to a cooling to rack to cool completely.
Once the cake is cooled, combine cream cheese and butter in large bowl and use an electric mixer to beat until creamy, and fluffy.
Add lemon juice and beat on low until mixed in.
With the mixer still on low, gradually add powdered sugar until fully combined. You can add more powdered sugar if you want a firmer texture.
Frost the cake and decorate the top with chopped nuts if desired.