Vegan carrot cake with non-vegan icing! But you can easily veganise the icing too if you wish. The oil helps to keep this cake moist.

2 c flour (I used spelt)
1 tsp baking powder
1 tsp baking soda
1/2 tsp salt
2 tsp cinnamon
1 tsp nutmeg
2 1/3 c grated carrot (250g)
1 c brown sugar or unrefined sugar
2 tbsp flaxmeal mixed wtih 6 tbsp water
1/2 c olive oil
1 tsp vanilla extract
1 tbsp apple cider vinegar
optional extras: 1 c chopped walnuts, 1/2 c raisins

For the icing:
100g softened butter or non-dairy spread
3 c icing sugar
3-4 tbsp lemon juice
2 tsp apple cider vinegar
150g softened cream cheese for non-vegan version
chopped walnuts to decorate if desired

Preheat oven to 180C. Line 2 x 22cm sponge tins with baking paper. You can also make muffins, mini muffins or a loaf with the batter.
In a large bowl sift all dry ingredients and mix well. Mix in carrot and sugar, and any optional extras. I personally like a plain carrot cake and sprinkle chopped walnuts on the icing. 
In a small bowl mix all the wet ingredients. Stir into dry ingredients. Don't overmix, then let sit for a few minutes to let carrots release all their water content. If the batter is still too thick or dry add a little bit of milk to loosen.
Spread evenly into your cake tins and bake for 25-30 or until cooked through. Leave in the tins for 10 minutes before turning out onto a wire rack to cool completely.
Mix all icing ingredients together until you achieve a spreadable consistency. Spread half onto one cake, put the other one on top and spread the rest on top. Sprinkle with chopped nuts if desired