Preheat the oven to 350 degrees fahrenheit (176 celsius).
Grease and line the bottom of two 9 inch pans with parchment paper. Alternatively grease the pans and flour the bottom and sides.
Mix the ground flax and water in a bowl and set aside.
Add the carrots, beets, dates, and walnuts (if desired) and process until fine but still chunky. Alternatively, finely grate carrots and beets, and finely dice dates and walnuts.
In a large bowl, mix all of the dry ingredients: flour, baking powder, cinnamon, ginger, nutmeg, salt, and date sugar.
In a small bowl, mix all of the wet ingredients: apple sauce, vanilla, and soy milk. Add the ground flax and water mixture and combine.
Pour the wet ingredients into the dry ingredients and mix until batter is smooth. Stir in the carrots, beets, dates, and walnuts.
Divide the batter between the cake pans for a layered cake (layers are thin). Alternatively, you can pour it all in one pan.
Bake until the tops of the cake layers are springy when touched and when a toothpick inserted into the center of the cake comes out clean, about 30-40 minutes.
Allow the cake to cool for about 15 minutes, then gently turn the pan over and slowly release the cake from the pan.
Prepare icing from my Protein Cream "Cheese" Icing recipe detailed above! Frost generously between the layered cakes, on top, and around.