In a large bowl or stand mixer, cream together the butter, brown sugar, and sugar until light and fluffy, about 1 minute.
Beat in the egg and zucchini, until just combined.
In a separate bowl, whisk together the flour, baking soda, cinnamon, and salt.
Add the dry ingredients to the wet ingredients, one half at a time, mixing until just combined.
Cover the cookie dough and place it in the fridge for at least 2 hours.
Preheat the oven to 375 degrees Fahrenheit. Line a baking sheet with parchment paper.
Use a medium scoop scoop to portion out 2 TBS sized cookie balls, and place them onto the prepared cookie sheet, 2 inches apart from each other.
Bake the cookies for 10 to 12 minutes, or until the tops of the cookies spring back when touched.
Allow the cookies to cool on the pan for a few minutes, then transfer them to a wire rack to cool completely.