Preheat oven to 350 F and lightly grease 2 8-inch cake pans.
In a large mixing bowl, mix together applesauce, butter, oil, sour cream, both sugars and eggs. Mix well.
In a separate bowl, sift together flour, baking soda, baking powder, salt, cinnamon, nutmeg and ground ginger. Add to egg mixture gradually. Mix well. Sifting the dry ingredients makes it easier to make sure every ingredient is mixed together well. If you don’t have a sifter, a metal strainer with very small holes will work just as good.
Using rubber spatula, fold in carrots and walnuts. Stir in vanilla.
Pour batter into baking pan and bake for 20-25 minutes until edges are golden.
In a large mixing bowl, beat butter, cream cheese and vanilla using an electric mixer on medium speed. Add sugar 1 cup at a time. Beat until smooth consistency.
Let cake cool completely before frosting. Remove from pan and cool on wire rack.
Frost cake and stick walnuts to sides of cake as garnish.