1. Preheat oven to 350 F and line 12 cup muffin pan with unbleached liners
2. In a large mixing bowl, whisk together carrots, applesauce, oil, vinegar and vanilla. Let sit for 10 minutes.
3. In another medium bowl, stir together all remaining ingredients. Pour wet into dry, then stir until just combined.
4. Using large cookie scoop, scoop batter into liners.
5. Bake 20 minutes or until a toothpick inserted into the cake comes out clean.
6. Cool in pan for 8 minutes and then moving to cooling rack to cool for 20 minutes.
7. While the cupcakes are cooling, beat butter and cream cheese until light and fluffy (about 5 minutes). Add Confectioner's Sugar and Vanilla Extract and beat until combined (1-2 minutes).
8. Place frosting in piping bag with Wilton 1M tip and swirl frosting onto cupcakes. Enjoy!