Make the flax egg mixture and place in the fridge to chill for 15 minutes.
Preheat the oven to 180c/350f.
Line a 12 cup muffin tin with cases.
Grate the carrot and set aside.
Mix the flour, cinnamon, nutmeg, sugar, bicarbonate of soda and salt.
Stir through the flax egg, applesauce and coconut oil.
Stir through the grated carrot.
Spoon a heaped tablespoon of mixture in to each case.
Bake for 20 minutes or until a toothpick inserted comes out clean. Allow to cool completely on a baking tray before icing.
Place the solid part of the coconut cream in to a bowl with the icing sugar and whip with a mixer until fluffy. Be patient, this make take a while! If your coconut cream is not chilled fully, you may find it hard to whip.