Preheat oven to 350F degrees. Line (2) 12 count muffin pan with cupcake liners. Set aside.
Using an electric or stand mixer, mix the eggs, canola oil, applesauce, brown sugar, and sugar until smooth.
In a medium bowl, whisk together flour, baking soda, baking powder, salt, nutmeg, and cinnamon until combined.
Slowly mix in dry ingredients to the wet ingredients until no clumps remain.
Stir in vanilla, carrots, pineapple and chopped walnuts.
Pour batter into the cupcake liners (about ¾ the way full). Bake for 20 minutes or until a toothpick inserted near the center comes out clean. Allow to cool before frosting.
MAKE THE CREAM CHEESE FROSTING:
Beat softened butter on medium speed with an electric or stand mixer. Beat for 3 minutes until smooth and creamy.
Add cream cheese, powdered sugar, heavy cream, salt and vanilla extract, increase to high speed and beat for 3 minutes.
Frost cooled cupcakes and top with chopped walnuts.
Notes
Store cupcakes in an airtight container at room temperature for up to 3 days and in the refrigerator for up to 5 days.