Wash, peel, and grate carrots. Place 18 cupcake liners in muffin tins. Preheat your oven to 350 degrees.
Whisk together flour, soda, baking powder, cinnamon, and salt in a small bowl. Set aside.
In a large mixing bowl, beat sugar, eggs, and oil with an electric mixer at medium-high speed till thick and foamy, 1-2 minutes. Add the sour cream, vanilla, and carrots and mix well. Add the dry ingredients and stir till just blended.
Fill paper lined cupcake pans half full of cupcake batter. Bake at 350° for 18-20 minutes. Let cool in the muffin tin for 3-5 minutes, then place cupcakes on a wire rack to cool completely.
For frosting, beat together cream cheese, butter, and brown sugar till smooth. Let sit for 5-10 minutes till brown sugar dissolves completely. Add vanilla, salt, and enough powdered sugar to make a frosting thick enough to pipe.
Transfer frosting into a piping bag. Use a large star tip to frost cooled cupcakes.