Preheat the oven to 350 F degrees and grease and flour three 7-inch cake pans. Set aside.
In a large bowl, whisk the brown sugar, oil, eggs and vanilla extract together until combined.
In another large bowl, whisk the gluten-free flour, baking powder, baking soda, salt, cinnamon, ginger, and nutmeg, until everything is well combined.
Pour the wet ingredients into the dry ingredients and using a spatula, fold the ingredients together until combined. Then, fold in the carrots and crushed walnuts.
Divide the batter evenly among the cake pans. Smooth the batter evenly into each pan with the back of a spoon.
Bake the cakes on 350F for about 25 to 30 minutes, or until a toothpick inserted into the middle comes out with only a few crumbs attached.
Allow cakes to cool in the pan for 10 minutes and turn out onto a wire rack to cool completely before frosting.