Preheat your oven to 350°F (175°C), and line your muffin tin with paper liners or lightly grease it.
In a large bowl, whisk the vegetable oil, sugar, eggs, and vanilla extract until the mixture is smooth and well combined.
Add in the milk (or buttermilk for extra tang) and mix well to keep the batter moist and help the muffins rise perfectly.
In a separate bowl, blend the cinnamon, nutmeg, ginger, cloves, salt, baking powder, and baking soda.
Gently fold the dry ingredients into the wet mixture, making sure not to overmix, this ensures your muffins stay light and airy.
Stir in the flour, then fold in the grated carrots for that moist, flavorful kick. If using coconut, add it now for extra texture and flavor.
Spoon the batter into the muffin tin, filling each cup approximately two-thirds of the way.
Optionally, sprinkle some extra coconut or cinnamon on top.
Bake for 25 minutes or until a toothpick inserted into the center comes out clean or with just a few crumbs.
Allow the muffins to sit in the tin for roughly 5 minutes before placing them on a wire rack to cool fully.
For the frosting, beat the butter and cream cheese until smooth, then add powdered sugar, lemon juice, and vanilla extract until light and fluffy.
Frost each muffin generously and top with extra coconut or grated carrots if you like.
Now, enjoy your carrot cake muffins with that creamy, irresistible frosting!