01 - Preheat oven to 350°F. Grease and line a 9x13-inch baking pan or two 8-inch round cake pans with parchment paper.
02 - Whisk together all-purpose flour, baking powder, baking soda, salt, cinnamon, nutmeg, ginger, and cloves in a large bowl.
03 - In a separate bowl, beat eggs with granulated and brown sugars until pale and thick. Incorporate vegetable oil, applesauce, and vanilla extract until smooth.
04 - Gradually fold the dry ingredient mixture into the wet ingredients until just combined.
05 - Gently fold in grated carrots, chopped walnuts, and optional raisins.
06 - Pour batter into prepared pans, smoothing the surface. Bake for 40 to 45 minutes or until a toothpick inserted in the center comes out clean.
07 - Allow cake to cool in pans for 15 minutes. Then invert onto a wire rack and cool completely.
08 - Beat softened cream cheese and butter until creamy. Add powdered sugar, vanilla extract, and salt; beat until smooth.
09 - Spread the frosting evenly over the cooled cake. For round pans, layer and frost as preferred.
10 - Optionally, sprinkle additional chopped walnuts over the frosting before serving.