01 - Preheat oven to 350°F. Line a 12-cup muffin tin with cupcake liners.
02 - In a medium bowl, whisk together flour, baking powder, baking soda, salt, cinnamon, nutmeg, and ginger.
03 - In a large bowl, whisk eggs, granulated sugar, and brown sugar until smooth. Add oil, applesauce, and vanilla extract; mix until well combined.
04 - Gradually fold dry ingredients into the wet mixture until just combined.
05 - Stir in grated carrots and nuts (if using) until evenly distributed.
06 - Divide batter evenly among cupcake liners, filling each about 2/3 full.
07 - Bake for 20-22 minutes, or until a toothpick inserted into the center comes out clean.
08 - Let cupcakes cool in the tin for 5 minutes, then transfer to a wire rack to cool completely.
09 - Beat cream cheese and butter together until smooth. Gradually add powdered sugar, vanilla, and salt; beat until light and fluffy.
10 - Once cupcakes are completely cool, frost generously and garnish with additional chopped nuts if desired.