1. Preheat oven to 350°F. Line a 24 count muffin tin with double paper liners. Set aside.
2. Combine flour, baking soda, baking powder, cinnamon, and salt. Set aside.
3. In a large bowl, beat oil, applesauce, brown sugar, granulated sugar, eggs, and vanilla extract until thoroughly combined. Add dry ingredients and beat until combined. Stir in carrots.
4. Divide batter evenly among 24 muffin cups. Bake for 18-20 minutes, until a toothpick inserted into the center comes out clean. Cool for 10 minutes, then remove cupcakes to a wire rack to cool completely.
1. In a stand mixer add cream cheese and 1 tablespoon water. Place on low speed until cream cheese is smooth. Slowly add in 1/2 cup of powdered sugar at a time with paddle attachment. Once the sugar is all added speed up mixer to medium. Once the cream cheese icing is thick and stands on it's own its ready.
If it doesn't stand on it's own add more sugar.
Place into a piping bag with star tip. Ice cupcakes. Keep refrigerated after icing.