Preheat your oven to 350°F (175°C). Grease an 8 × 8-inch baking pan or line it with parchment paper.
In a large mixing bowl, whisk together the shredded zucchini, granulated sugar, oil, and eggs until everything is well combined.
In a separate bowl, mix the all-purpose flour, ground cinnamon, salt, baking powder, and baking soda.
Gradually add the dry ingredients to the wet mixture. Stir gently until just combined, being careful not to overmix.
Pour the batter into the prepared baking pan and spread it evenly with a spatula.
Place in the preheated oven and bake for 28–32 minutes, or until the center is set and a toothpick inserted into the middle comes out clean or with a few moist crumbs.
Remove the cake from the oven and allow it to cool completely before adding the frosting.
In a medium bowl, beat the softened cream cheese and butter together until smooth and creamy.
Mix in the vanilla extract, powdered sugar, and 1 tablespoon of milk or cream. Beat until fluffy, adding a little more milk if needed to reach your desired consistency.
Spread the cream cheese frosting evenly over the completely cooled cake.
Cut into squares and enjoy your delicious homemade zucchini cake!
