How to Make the Cupcakes

1. Preheat oven to 375°F. Line cupcake pans with cupcake liners and set them aside.
2. In a medium mixing bowl, whisk together the flour, baking soda, baking powder, cinnamon, nutmeg, and salt. 
3. In a separate bowl with a hand mixer, combine the sugar, apple sauce,  oil, and vanilla at medium speed. Slowly mix in one egg at a time until each egg is incorporated.
4. Adjust the mixer speed to low and slowly add the flour mixture. Mix in the carrots and nuts.
5. Fill the cupcake liners 3/4 full with batter. Bake them for 5 minutes at 375°F  and then turn the oven down to 350°F. Finish baking the cupcakes for 13-15 minutes or until you can insert a toothpick into the middle of the cupcake and it comes out clean.
6. Cool the cupcakes before frosting them.

How to Make the Frosting

1. Beat the cream cheese and butter in a bowl until well combined. Adjust the mixer speed to low and slowly add the powdered sugar. Stir in the vanilla and mix just until well combined.
2. Place a large star tip in your piping bag and fill the bag with frosting. Pipe the frosting onto your cooled cupcakes. Sprinkle the chopped walnuts onto the frosting.
3. If you don’t have a piping bag, you can also spoon the frosting onto the cupcakes and use an offset spatula or dinner knife to spread it.