Set oven to 350F. Grease a 9x13 pan with EVOO and line with parchment paper. Grate your carrots finely (takes me about 6 large carrots to get about 2 cups).
Get two large mixing bowls. In one, pour in coconut milk and apple cider vinegar. Mix with a whisk for about 30 seconds then let rest.
n separate bowl, mix in flour, brown sugar, baking powder, baking soda, cinnamon and salt. Mix with a hand mixer on medium for about 2 minutes.
In your coconut mixture bowl, add in canola oil, applesauce, vanilla extract then finally the carrots. Mix with a hand mixture on low for about 1-2 minutes (don’t want to over mix). Combine bowls. Again, using a hand mixer, blend together on low for about a minute.
In a clean bowl, add Daiya vegan cream cheese and earth balance butter. Mix using your hand mixter, 2 minutes on medium until nice and creamy. Add in powered sugar and maple syrup. Blend some more until a nice and creamy. Add in more powdered sugar to taste and blend again if needed. I like to refrigerate my frosting until a few minutes before I’m ready to use it.
Pour into your pan and bake for about 30 - 35 minutes until a toothpick comes out clean. Let fully cool before frosting your cake. Then, finally sprinkle on the shredded coconut and viola! Enjoy!