Preheat your oven to 350° and get your mixer ready. In your mixer bowl, beat your eggs for about 1 minute. Mix in your oil, sugar, baking powder, baking soda, salt for about 2 minutes. Then gradually add in your flour and beat until mixed.
Once you've got all the above mixed together, it's time to mix in your carrots. Slowly add the carrots to bowl and mix until combined. *Make sure you're using finely shredded carrots so they don't sink to the bottom while baking.
Place baking liners into your pan and carefully fill them 3/4 full of the carrot mix. Bake in a preheated oven for about 20-24 minutes or until a toothpick comes out clean. After done baking, remove from oven and let cool completely.
While the cupcakes are baking, begin making the cream cheese frosting. In a medium sized bowl add the butter, cream cheese and vanilla mix for about 2 minutes. Gradually add in your powdered sugar and heavy whipping cream, mix for another 2-4 minutes or until it's completely mixed and beginning to fluff up. If you like your frosting really fluffy mix a little longer.