Preheat the oven to 180ºC (350ºF) and line a regular cupcake tin with 9 paper liners.
Tip the flour, baking powder, baking soda, salt, cinnamon, nutmeg, and ginger into a medium bowl and whisk well. Set aside.
To another bowl, add the coconut sugar, yoghurt, oil, vanilla, and egg. Whisk well to combine.
Add half of the dry ingredients to the wet ingredients and whisk together until a few streaks of flour remain. Add the second half of the dry ingredients and whisk again until smooth. Fold in the shredded carrot.
Divide the batter evenly between the 9 paper cases. The cases should only be about half way full; do not exceed the ⅔ full mark.
Bake the cupcakes for 15-17 minutes, or until a toothpick inserted comes out clean. Leave them to cool on a wire rack while you make the frosting.