Preheat oven to 350°F (177°C). Line two standard 12-count muffin pans with 14 cupcake liners and set aside.
In a mixing bowl, whisk together the flour, baking powder, baking soda, cinnamon, ginger, nutmeg, and salt until well combined. Set aside.
In a separate large mixing bowl, whisk together the oil, brown sugar, granulated sugar, applesauce, eggs, and vanilla extract until fully combined. Stir in the grated carrots.
Add the dry ingredients to the wet ingredients and mix until just combined. Then stir in the chopped nuts and raisins.
Evenly distribute the batter between all 14 cupcake liners, only filling each liner about 2/3 of the way full. Bake in separate batches at 350°F (177°C) for 16-20 minutes or until the tops of the cupcakes are set and a toothpick inserted into the center comes out clean.
Carefully remove the cupcakes from the oven and allow to cool slightly for 2-3 minutes in the pans. Then, carefully remove the cupcakes from the pans and transfer to a wire rack to cool completely.
To make the cream cheese frosting:
In the bowl of a stand mixer fitted with the paddle attachment, or in a large mixing bowl using an electric handheld mixer, beat the cream cheese and butter together for about 1-2 minutes or until smooth.
Add the powdered sugar and vanilla extract and continue mixing until fully combined, stopping to scrape down the sides of the bowl as needed.
Once the cupcakes have cooled completely, frost as desired, serve, and enjoy!
Notes
The frosted cupcakes may be stored in an airtight container in the refrigerator for up to 4 days. Freezing Instructions: Cupcakes will freeze well for up to 3 months, thaw overnight in the refrigerator, and bring to room temperature before frosting.Frosting will also freeze well for up to 3 months, thaw overnight in the refrigerator, bring to room temperature and mix well before frosting the cupcakes.