Preheat the oven to 350 degrees F. Lightly coat a baking sheet with nonstick spray or line with parchment paper or silpat mats. Place the shredded zucchini between layers of paper towel, then thoroughly squeeze out as much excess water as possible. Set aside.
In the bowl of a stand mixer fitted with the paddle attachment or a large mixing bowl, beat the butter on high until completely smooth and creamy, about 2 minutes. Add the coconut sugar and beat on medium high for 3 full additional minutes, stopping to scrape down the bowl as needed. On high speed, beat in the honey and Greek yogurt, then the egg and vanilla until completely combined. The mixture may look curdled, but it will be fine. Scrape down the mixer as needed and blend the batter as well as you can.
In a separate bowl, whisk together the whole wheat flour, oats, baking powder, salt, baking soda, cinnamon, and cloves. On low speed, slowly add one-third of the dry ingredients to the wet. By hand, fold in half of the shredded zucchini. Mix in the next third of the dry ingredients (again on low speed), fold in the remaining zucchini, and finally mix in the last third of the dry ingredients. By hand, stir in the chocolate chips.
With a cookie scoop, portion the cookies onto the prepared baking sheets. Bake for 11 to 13 minutes, until the tops are barely set and the edges are dry to the touch. They may seem underdone, but do not overbake or the cookies will be dry. Let rest on the pan for 5 minutes, then transfer to a wire rack to cool completely.
Batter can be prepared and stored tightly covered in the refrigerator up to 1 day in advance.
Store leftovers at room temperature in a paper-towel-lined airtight container for up to 1 week or freeze, tightly wrapped, for up to 3 months. Let thaw overnight in the refrigerator or at room temperature.
To make the cookies gluten free: I have not yet experimented, but I think you could successfully replace the white whole wheat flour with gluten-free oat flour, adding an additional 2 to 3 tablespoons if the cookie batter seems too wet. An all-purpose gluten-free flour blend like this onewould also work well. Ensure your quick oats are certified gluten free, like these are. OR make my Carrot Cookies, using zucchini instead of carrots.
To make vegan: I have not yet tried the recipe this way, but I think you could use a vegan buttery spread in place of the unsalted butter, replace the honey with maple syrup, the egg with a flax egg, and the Greek yogurt with a nondairy yogurt.