Preheat oven to 350 degrees F (176 C). Butter and flour two 8-inch, 1 9x13-inch, or 3 6-inch round pans with coconut oil or vegan cooking spray and dust with gluten-free flour (adjust number/size of pans if altering batch size). Shake out excess. Set aside.
Prepare flax eggs in a large mixing bowl. To flax eggs, add oil and maple syrup and whisk to combine. Next, add applesauce, sugars, salt, baking soda, baking powder, and cinnamon and whisk to combine.
Add lesser amount of almond milk (3/4 cup or 180 ml as original recipe is written // adjust if altering batch size) and stir. Add grated carrot and stir. Then add almond flour and gluten-free flour blend and stir. The batter should be thick but pourable. If too thick, add remaining almond milk 1/4 cup or 60 ml as original recipe is written // adjust if altering batch size). If adding walnuts, add at this time and stir.
Divide evenly among cake pan(s). Bake for 40-50 minutes or until deep golden brown and a toothpick inserted into the center comes out clean. When you press on the top, it shouldn’t feel too spongy, so don’t be afraid of over-baking! The gluten-free blend just takes a little longer to bake. Also, note that the size of pan you use will vary baking time.
Remove from oven and let rest in the pans for 15 minutes. Then carefully run a knife along the edges and gently invert onto cooling racks to let cool completely.
NOTE: This cake needs to cool completely. It benefits from plenty of airflow, and the flavors develop as the cooling process goes on. If short on time, you can speed the cooling by placing the cakes in the refrigerator or freezer until very cool to the touch.
Once cooled, you can serve as is or frost! For frosting, you have several options! See options above.
Store leftovers at room temperature, covered, for 2-3 days, in the refrigerator for 3-4 days, or covered well in the freezer for several weeks. However, it's best when eaten fresh.
Do note that, if using vegan cream cheese or yogurt in the frosting, the cake should be stored in the refrigerator. From the refrigerator, let set out for 10-15 minutes before serving so it warms a bit and becomes more tender. Let thaw completely from the freezer.
*If avoiding oil, sub extra applesauce. The cake may not be quite as moist and may not bake up as nicely, however, so proceed with caution. *I used brown and cane sugars because they provided the best texture (fluffy and tender) for the cake. I also tested with coconut sugar, and although it was sweet enough, the texture was more dense. But, if coconut sugar is preferred, it still turns out well! *If almond/nut-free, sub the almond milk for rice, hemp, or light coconut milk. And sub the almond flour for another nut/seed flour (such as hazelnut, sunflower seed, or brazil nut). If you can't tolerate nuts or seeds, try subbing more gluten-free flour blend or oat flour. And omit the walnuts or sub raisins. *I used my go-to gluten-free flour blend. If subbing your own blend, know that the results may vary. *Recipe adapted from my Vegan Carrot Apple Muffins. *Nutrition information is a rough estimate calculated without frosting.