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.