Preheat your oven to 350°F (177°C) and line a standard 12-cup muffin tin with cupcake liners. In a large mixing bowl, combine the flour, baking powder, baking soda, salt, cinnamon, ginger, and nutmeg by whisking them together thoroughly. Set this dry mixture aside. In a separate bowl, whisk together the vegetable oil, packed brown sugar, eggs, applesauce (or sour cream or yogurt), and vanilla extract until smooth and well combined. Stir in the shredded carrots. Add the wet mixture to the bowl of dry ingredients and gently fold or whisk everything together until the batter is fully incorporated. The consistency should be slightly thick.
Spoon or pour the batter into the prepared cupcake liners, filling each about three-quarters full to prevent overflow during baking. Bake for 21 to 23 minutes, or until a toothpick inserted in the center of a cupcake comes out clean. If making mini cupcakes (about 30 total), bake for 12 to 13 minutes at the same temperature. Allow the cupcakes to cool completely on a wire rack before applying frosting.
To prepare the cream cheese frosting, use a handheld or stand mixer fitted with a paddle or whisk attachment. Beat the softened cream cheese and butter together on high speed in a large bowl until the mixture is smooth and creamy. Add the confectioners’ sugar, vanilla extract, and salt. Begin beating on low speed for about 30 seconds, then switch to high speed and continue beating for 2 full minutes until fluffy. If you’re planning to pipe the frosting, cover the bowl and refrigerate it while the cupcakes finish cooling—chilled frosting holds its shape better for decorating.
Once the cupcakes have cooled completely, frost them as desired and add any optional garnishes, such as chopped nuts or white chocolate carrot toppers. For a polished look, you can use a large round piping tip like the Ateco 808 and finish with a swirl using a small offset spatula, though that’s entirely optional. Store any leftover frosted cupcakes in an airtight container in the refrigerator for up to 5 days. A cupcake carrier is ideal for keeping them fresh and secure, especially if you’re transporting them.