Preheat your oven to 350°F and grease a 9x13 inch baking pan.
In a large bowl, whisk together the gluten-free flour, baking soda, salt, cinnamon, nutmeg, and ginger.
In another bowl, whisk together the oil, applesauce, brown sugar, maple syrup, non-dairy milk, and vanilla extract.
Add the wet ingredients to the dry ingredients and stir until well combined.
Fold in the carrots and walnuts (if using).
Pour the batter into the prepared pan and spread it evenly.
Bake for 25 to 30 minutes or until a toothpick inserted in the center comes out clean.
Let the cake cool completely before frosting with your favorite vegan cream cheese frosting.