Preheat your oven to 350°F (175°C). Grease a 9x13-inch baking pan or line it with parchment paper.
In a medium bowl, combine the flour, baking powder, baking soda, spices, and salt.
In a large bowl, whisk together the granulated sugar, brown sugar, and vegetable oil until well combined.
Add the eggs and vanilla extract, mixing until smooth.
Gradually add the dry ingredients to the wet ingredients, stirring until just combined.
Fold in the grated zucchini until evenly distributed.
Pour the batter into the prepared baking pan and spread it evenly.
Bake for 25-30 minutes, or until a toothpick inserted in the center comes out clean.
Allow the bars to cool completely in the pan on a wire rack.
For the frosting, beat the softened cream cheese and butter together until creamy.
Gradually add the powdered sugar and vanilla extract, mixing until smooth.
If the frosting is too thick, add milk one tablespoon at a time until desired consistency is reached.
Once the bars are completely cool, spread the frosting evenly over the top.
Cut into squares and serve.