Preheat your oven to 350°F (175°C).
Grease an 8 or 9 inch round cake pan and line the bottom with a circle of parchment paper.
In a large bowl, whisk together the flour, baking soda, baking powder, salt, cinnamon, and ginger.
Add shredded carrots and toss to coat. Make a well in the center of the dry ingredients.
Add the sugar, canola oil, vanilla extract, apple cider vinegar, applesauce, and water to the well. Stir until well mixed.
Pour the batter into the prepared pan.
Bake for about 35 minutes, or until a toothpick inserted in the center comes out clean.
Let the cake cool in the pan for about 15 minutes. Then, run a knife around the edge of the pan, remove the cake, and invert it onto a wire rack to cool completely.
Once the cake is completely cooled, start making the frosting:
In a mixing bowl, whip the Daiya cream cheese and vegan butter together.
Sift in the powdered sugar and blend until creamy and smooth.
Frost the cooled cake. Refrigerate if not serving immediately. Keep any leftover cake in the refrigerator.