Preheat oven to 350° F. Line a 9x13 metal baking pan with parchment paper. Set aside.
In a large bowl, whisk together the flour, baking powder, baking soda, salt, cinnamon and ground cloves. Set aside.
In a separate large bowl, vigorously whisk together the eggs, sugar and brown sugar until light in color and well combined. Add vegetable oil, applesauce and vanilla extract. Whisk until combined.
Add dry ingredients to wet ingredients and mix just until combined (it’s ok if there are still a couple flour pockets). Add shredded zucchini and stir until evenly dispersed.
Transfer batter to prepared baking pan and spread into an even layer. Bake at 350 F for 35 to 45 minutes or until a toothpick inserted in the center comes out clean. Let the cake cool in the pan completely.
For the frosting, beat cream cheese and butter together on high speed until smooth and creamy, about 2 minutes. Add confectioners’ sugar and salt, then mix on medium speed until combined. Add vanilla and mix until combined. Scraping down the bottom and sides of the bowl as necessary.
Spread frosting over cooled cake. Garnish with chopped walnuts, slice and serve.
Notes
Zucchini should be shredded, then patted dry with a clean cloth to remove any excess liquid.Store covered in the refrigerator for up to 5 days. Serve at room temperature.Freeze for up to 3 months. Wrap in plastic wrap and aluminum foil to prevent freezer burn. Freeze, then defrost in the refrigerator before bringing to room temperature and serving.