Preheat your oven to 350 °F (177 °C). Line the bottom of 2 8-inch Cake Pans with parchment paper and lightly grease the sides.
Combine the ground flax and water in a small bowl. Set aside for 10 min. It will thicken and gel up a bit.
In a medium mixing bowl, add the soy milk and apple cider vinegar. Combine and let it sit for 10 minutes to create vegan buttermilk. It will thicken and curdle slightly. Set aside.
In a large mixing bowl whisk together the flour, baking powder, baking soda, cinnamon, ginger, nutmeg, and salt. Set aside.
In the medium bowl with the buttermilk, add the oil, applesauce, white and brown sugar, prepared flax egg, and vanilla. Whisk to combine well.
Now slowly pour the wet ingredients into the larger bowl of dry ingredients. Whisk until almost combined. Now gently fold in the carrots and walnuts until combined.
Divide batter between both pans and place in the oven for 35-45 minutes. To check for doneness, lightly press the surface - It should spring back without leaving an indent. You can also insert a toothpick in the middle - it should be clear of wet batter, but some dry crumbs are fine
Let the cake cool in the pans for 10-15 minutes before removing. Then let them cool on a rack completely before frosting. Frost and top decorate with chopped walnuts.
Notes
Nutritional info doesn't include the frosting. That information is in that recipe card. Instead of Vegan Cream Cheese Frosting, you can try my Vegan Buttercream Frosting recipe. Measuring Flour - For accurate results, don't scoop the flour with a measuring cup directly from the flour container. Instead, aerate it first, then scoop the flour out of your container with a spoon and then into a measuring cup. Don't pack or tap the cup. After filling, lightly sweep a butter knife across the top to remove the excess flour.I do not recommend matchstick carrots for this recipe. Finely grated carrots provide moisture and they soften better during baking. Make sure the baking powder and baking soda are not expired. Fresh leavening agents are important for a successful baking experience.You can also make this in two 9-inch cake pans. Bake for 30-40 minutes.Raisins are a nice addition too. Just decrease the walnuts to ½ cup and add ½ cup of raisins. You can also just swap out the walnuts for raisins or omit the add-ins altogether.