Preheat oven to 350℉—grease 2 nine-inch round baking pans, and set aside.
In a large bowl, mix together brown rice flour, almond flour, sugar, spices, baking powder, and salt.
In another bowl, mix together coconut oil, ground flax seeds, crushed pineapple, applesauce, and vanilla.
Mix dry ingredients into bowl with wet ingredients, and stir to fully combine.
Fold in a 1/2 cup of the walnuts and the carrots.
Divide the cake batters evenly between the two pans. Bake for about 50 minutes or until a toothpick inserted in the center of the cake comes out clean.
Cool completely before adding frosting.