Preheat the oven to 350℉/176℃. Line a 9x9 baking pan with parchment paper and set aside. Grate the zucchini and set aside for use later.
In a large bowl, add the flour, baking soda, baking powder, cinnamon, nutmeg, cloves, cornstarch, and salt. Stir to combine, and set aside.
1 3/4 cups all-purpose flour, 3/4 tsp baking soda, 1 tsp baking powder, 1/4 tsp salt, 1 tbsp cornstarch, 1 1/2 tsps cinnamon, 1/8 tsp nutmeg, Pinch of cloves
In a large bowl, add oil, brown sugar, and white sugar. Whisk for 2-3 minutes.
1/2 cup light brown sugar, 1/2 cup oil, 1/3 cup white sugar*
Add in the eggs and vanilla, and continue whisking until well combined.
2 large eggs, 1 tbsp vanilla
Add in the applesauce and sour cream. Whisk together, scraping the bowl as needed.
1/2 cup unsweetened applesauce, 1/3 cup sour cream
Add in the dry ingredients, and gently with a spatula, mix in, but not completely just yet.
Add in the shredded zucchini, and then mix together just until the flour streaks disappear. Do not over-mix!
1 1/2 cups shredded zucchini
Transfer into a prepared pan and spread evenly. Bake for 45-55 minutes or until a toothpick inserted comes out clean.
While the cake cools, make the frosting. Into a bowl add the butter and lemon zest. Beat on medium-high speed for 2-3 minutes until light and pale in colour. Add in the sour cream, and continue beating for another 2-3 minutes. Add in the powdered sugar and mix together until smooth (start with 2 cups, and add more until desired consistency is reached).
1/2 cup unsalted butter, 1/3 cup sour cream, Zest from 1 small lemon, 2-3 cups powdered sugar
Top the cooled cake with the frosting, slice, and enjoy! When not consuming, store this cake in the refrigerator in an airtight container.