Preheat the oven to 350°F (180°C) and begin greasing your cake pan.
Sift the flour, baking powder, baking soda, salt, cinnamon and nutmeg into a mixing bowl. Add in your grated carrot and brown sugar into your mixing bowl.
Prepare your flax eggs, by mixing 2tbsp Flaxseed Meal with 6 tbsp water, allowing the mixture to sit for a minute.
In the meantime, add in your canola oil and apple cider vinegar to the mixing bowl. Once your flax eggs are ready, add them to the mixing bowl with your oil and apple cider vinegar.
Add your mixture to the larger mixing bowl with your carrots and flour. Have a little patience and let the batter sit for a minute or two so that the carrots can release more water into the batter to enable you to mix it all together.
*If your batter is still too dry to mix after letting it sit for a couple of minutes (and only if it’s too dry to mix after sitting for a few minutes) then add in a little of your preferred non-dairy milk. Only add as much as you need to get the batter to a wet enough consistency so that it can mix properly.
You may mix chopped walnut into your batter mixture for some extra texture, but this is optional.
Place your mixture into your greased cake pan and place into the oven to bake for 30 minutes, or until a toothpick inserted into the center comes out clean.
Set your cake onto a cooling rack and begin preparing your frosting.
Mix your softened cream cheese, powdered sugar, and lemon juice in a stand mixer with a whisk attachment until it becomes creamy and fluffy in texture.
Decorate your carrot cake immediately or place in the fridge for a firmer frosting to work with.