Heat oven to 350 degrees F. Grease 12 muffin tins or line with cupcake liners and set aside.
In a large bowl, beat the Eggs for a few seconds. Gently stir in the Grated Carrots and Oil.
Add the rest of the ingredients: Flour, Sugar, Cinnamon, Baking Soda, Baking Powder, Salt. Stir to combine, about 10 stirs (be careful not to over mix!).
Fill cupcake tins about 2/3 full. Bake for no more than 18 to 20 minutes or until golden brown. Remove from oven and allow to cool for at least 10 minutes before frosting.
In a blender or by hand, beat the Butter, Cream Cheese, and Vanilla until fluffy and combined.
Gradually add the Powdered Sugar and Heavy Cream until light and fluffy.
Once the cupcakes have cooled, frost them with the cream cheese frosting using a piping bag, zip-lock bag, or spread with a spoon.
