Preheat oven to 350 degrees.
Spray a large cookie sheet or baking sheet (15x10x1-inch) with non-stick cooking spray and set aside.
Peel zucchini, cut out the seeds, and cut into large chunks. Throw the chunks into a blender and blend until it turns into a "puree" - you will need about 1 1/2 cups of puree for this cake. Set zucchini puree aside.
In a mixing bowl, cream butter, sugar, and milk together. Add in eggs, zucchini puree, and vanilla and mix again until all combined.
In another mixing bowl, whisk flour, baking soda, cinnamon, salt, nutmeg, and cloves together. Add the dry ingredients in with the wet zucchini ingredients and mix until they are just combined (don't over mix).
Pour the cake batter into the prepared pan and spread it around the pan evenly using a spatula.
Place pan in the pre-heated oven and bake for 14-18 minutes or until a toothpick inserted in the center comes out clean.
Remove cake from the oven and allow it to cool completely.
To make frosting, beat cream cheese, butter, and vanilla together in a bowl. Add in a pinch of salt and powdered sugar and mix well. Add a little bit of milk until it reaches the desired consistency you are looking for (you will want to be sure that it's easy to spread onto the cake, but not too thin that it's runny).
You can serve this cake at room temperature or for a cold treat, stick it in the fridge until you serve.