Preheat the oven to 350°F (175°C).

In a mixing bowl, cream together the softened butter, brown sugar, and granulated sugar until light and fluffy.

Add the egg and vanilla extract, mixing until well combined.

In another bowl, whisk together the flour, baking soda, cinnamon, and salt.

Gradually add the dry ingredients to the wet ingredients, mixing until just combined.

Fold in the grated zucchini.

Drop spoonfuls of dough onto a baking sheet lined with parchment paper.

Bake in the preheated oven for 12-15 minutes, or until the edges are lightly golden.

Remove from the oven and let cool on the baking sheet for a few minutes before transferring to a wire rack to cool completely.

In a mixing bowl, beat together the softened cream cheese and butter until smooth.

Gradually add the powdered sugar and vanilla extract, mixing until well combined and fluffy.

Once the cookies are completely cooled, spread a generous amount of cream cheese frosting on top of each cookie.

Serve and enjoy!