Preheat your oven to 350°F. Line a cupcake pan with 12 paper liners. Set aside.
To start the cupcakes, combine the vegetable oil, sugars, applesauce, eggs, vanilla extract, and milk in a large bowl. Whisk until the mixture is smooth. Then, add in the shredded carrots and mix to combine.
To the bowl, add in the flour, baking soda, baking powder, salt, and spices. Mix until everything is just combined and there are no more floury bits. Be sure not to overmix the batter.
Scoop or pour the batter equally into the 12 lined cupcake liners. Bake for 20-21 minutes. The cupcakes should have rounded tops, and a toothpick should come out clean. Allow the cupcakes to cool completely before frosting them.
Once the cupcakes are cool, make the frosting. Start by creaming together the softened cream cheese and unsalted butter. Cream for about 2 minutes until light and fluffy. Add in the powdered sugar, vanilla extract, cinnamon, and a pinch of salt. Beat for another 2 minutes or so, until the frosting is light and fluffy. If you want your frosting a little thinner, add a tablespoon of heavy cream and whip it again until incorporated.
Pipe or spread the cream cheese frosting onto the cooled cupcakes. Serve as is, or top with chopped nuts or a sprinkle of cinnamon, if desired. Enjoy!
Notes
*1 tablespoon heavy cream is optional for the frosting. If you want your frosting a little thinner, add a tablespoon of heavy cream and whip it again until incorporated.