Preheat the oven to 350°F (175°C) and line a 12-cup muffin tin with cupcake liners.
In a medium bowl, whisk together the all-purpose flour, baking soda, salt, cinnamon, nutmeg, and ginger. Set aside.
In a large mixing bowl, beat the canola oil and light brown sugar until smooth.
Add the eggs one at a time, mixing well after each addition. Stir in the unsweetened applesauce and vanilla extract.
Gradually add the dry ingredients to the wet mixture, stirring until just combined.
Fold in the shredded carrots and ¼ cup of the chopped walnuts.
Divide the batter evenly among the cupcake liners, filling each about two-thirds full.
Bake for 18-22 minutes, or until a toothpick inserted into the center comes out clean.
Let the cupcakes cool in the pan for 5 minutes before transferring them to a wire rack to cool completely.
To make the frosting, beat the cream cheese and butter together until smooth and fluffy.
Mix in the vanilla extract, then gradually add the powdered sugar, beating until creamy and well combined.
Once the cupcakes are fully cooled, frost them generously with the cream cheese frosting.
Sprinkle the remaining 2 tablespoons of chopped walnuts over the top for extra crunch and decoration.
Serve and enjoy these deliciously spiced carrot cupcakes!