For the cupcakes: 

1. Preheat oven to 350°F (177°C) and line muffin pan with extra-large baking cups.
2. Mix all dry ingredients together with a spoon.
3. Whisk wet ingredients together until frothy.
4. Add the wet ingredients to the dry ingredients and stir until mixed, then fold in the grated carrots.
5. Pour the batter into the baking cups, filling them 1-2cm from the top of the baking cup. Cook for 25 minutes or until the toothpick inserted in the center comes out clean.
6. Let the cupcakes cool for 30 minutes, then ice them with the Coconut Cream Cheese icing.

For the icing: 

1. To make the icing sugar, process golden cane sugar in a food processor.
2. The coconut oil should be a buttery consistency at room temperature, if it is rock hard you may need to gently soften it. Cream the coconut oil, vanilla, salt, and icing sugar together.
3. Add the apple cider vinegar and mix. Slowly add the milk until the desired consistency is reached at room temperature. The coconut oil will liquefy at 24°C, so to ensure the proper consistency is reached, prepare the filling at the same temperature it will be served in, adjusting the consistency by adding milk or additional icing sugar.
4. Spread the Coconut Cream Cheese Icing on the cupcakes using a knife or piping bag.
5. To make the sprinkles, process half of a carrot until you get little sprinkle-like pieces of carrot and sprinkle them over the iced Carrot Cake Cupcakes.