1. Preheat the oven to 350°F (175°C) and line a muffin pan with paper liners.
2. In a bowl, mix flour, baking soda, baking powder, cinnamon, and salt.
3. In another bowl, mix brown sugar, white sugar, oil, applesauce, eggs, and vanilla.
4. Add dry ingredients to wet ingredients and stir gently.
5. Fold in the grated carrots.
6. Fill cupcake liners about 3/4 full with batter.
7. Bake for 18 to 20 minutes until a toothpick comes out clean.
8. Let cupcakes cool completely.
9. Beat cream cheese and butter until smooth.
10. Add brown sugar, powdered sugar, and vanilla. Mix until creamy.
11. Frost the cooled cupcakes and serve.
Prep Time: 20 minutes
Cooking Time: 20 minutes
Total Time: 40 minutes
Servings: 12 cupcakes
