Add the vegetable oil and sugar to a mixing bowl and whisk until well combined.
Add the egg and mix until smooth.
Add the buttermilk and mix until incorporated.
In a separate bowl, combine the flour, cocoa powder, baking powder, baking soda, salt, ginger, nutmeg, and cloves.
Add the dry ingredients to the wet mixture and whisk until combined.
Add the grated carrots and mix until evenly incorporated.
Add the cinnamon and mix well.
Divide the batter evenly among the lined cupcake cups.
Bake at 350°F (175°C) for 17–22 minutes, or until a toothpick inserted into the center comes out clean.
Remove from the oven and allow the cupcakes to cool completely.
Beat the cream cheese, butter, powdered sugar, cinnamon, and vanilla extract until smooth, creamy, and fluffy.
Transfer the frosting to a piping bag and pipe it onto the cooled cupcakes.
Serve the chocolate carrot cake cupcakes.
