Cream butter and sugars until fluffy, about two minutes.
Add eggs and vanilla.Beat two more minutes.
Add baking soda, baking powder, and salt. Mix for one minute.
Add cocoa and flour. Beat just until combined. The dough will be stiff.
Add grated zucchini and chocolate chips. Mix only until incorporated. As the dough sits the zucchini will start releasing some of the water in it and the dough will become thinner and "wetter". The last batch of cookies might be flatter than the first, because of the amount of time the zucchini sits in the cookie dough before baking.
Drop dough onto a parchment-lined baking sheet in 2 Tablespoon sized cookies.
Bake for 10-11 minutes. Be careful to not over bake.
Let cookies cool on the sheet of a minute, then remove to a cookie rack to finish cooling.
Notes
Use other types of chocolate chips; white, butterscotch, peanut butter, milk, or semi-sweet. Even a combination would be great!You can peel zucchini if you'd like, but you don't have to. It's great either way. You'll be able to see it better if it's not peeled. Course grate zucchini.