Preheat the oven to 350° F. Line two cupcake pans with paper liners.
In a medium mixing bowl, combine the flour, baking powder, baking soda, spices and salt; whisk together and set aside. Shred the carrots (you should have about 3 cups) into the bowl with the dry ingredients and set aside.
In a large bowl, whisk the sugars and eggs until frothy and thoroughly combined, about 1 minute. Add the oil. Stir in the carrots and dry ingredients until incorporated and no streaks of flour remain.
Scoop evenly into the prepared cupcake liners. Bake for 20-24 minutes or until a toothpick inserted in the center comes out clean. Let cool in the pan at least 5 minutes, then transfer to a wire rack to cool completely.
To make the frosting, beat the cream cheese and butter on medium speed until well combined and smooth, about 2-3 minutes. Mix in the vanilla extract. Gradually beat in the confectioners’ sugar until totally incorporated, increase the speed and then beat until smooth. Frost cooled cupcakes as desired. (I used a Wilton 1M tip for my pastry bag)