Preheat your oven to 180°C (350°F) and line a muffin tin with paper cupcake liners.
In a large bowl, whisk together the shredded carrot, flour, sugar, and baking soda.
Add the milk, oil, vanilla to the dry ingredients. Mix gently until just combined. The batter will be slightly thick and speckled with bright orange carrot bits.
Spoon the batter into the cupcake liners, filling each about ¾ full. You can also use a piping bag to fill in the cupcakes more easily.
Bake for 18–22 minutes, or until a toothpick inserted in the center comes out clean. Let the cupcakes cool completely before frosting.
For the frosting, beat your chosen ingredients until smooth and fluffy.
Once the cupcakes are cool, spread a generous dollop on each one, then finish with a light sprinkle of brown sugar.
