Preheat your oven to 350°F and get your 12-cup muffin pan ready by lining it with cupcake liners.
Take a large bowl and whisk together the flour, baking powder, baking soda, salt, cinnamon, ginger, and nutmeg. In another bowl, combine the oil, brown sugar, eggs, applesauce, and vanilla extract. Stir in the carrots. Now, merge the wet and dry ingredients until you have a thick batter.
Fill the cupcake liners with batter, about 3/4 full to prevent overflow. Bake for 21-23 minutes or until a toothpick comes out clean. Let them cool off completely before you frost.
For the frosting, beat the cream cheese and butter until creamy. Add in the confectioners’ sugar, vanilla extract, and a pinch of salt. Start slow, then ramp up the speed and beat for 2 minutes. If you're using a piping bag later, chill the frosting.
Once the cupcakes are cool, frost them and add any garnishes you like. Store any leftovers in the fridge.