Carrot Cake Cupcakes:

4 large eggs
3/4 cup canola oil
1/2 cup applesauce
1 cup golden brown sugar
1 cup granulated sugar
2 cups all-purpose flour
2 teaspoons baking soda
2 teaspoons baking powder
1/2 teaspoon salt
1/4 teaspoon nutmeg
3 teaspoons ground cinnamon
3 teaspoons vanilla extract
3 cups grated carrots
1 cup crushed pineapple, drained
1 cup chopped walnuts

Cream Cheese Frosting:

1 cup butter, softened
1 (8oz) package cream cheese, softened
4 cups powered sugar
¼ teaspoon salt
1 tablespoon vanilla
2 tablespoons heavy whipping cream
1/4 cup chopped walnuts