Shred and squeeze the zucchini: Grate the zucchini on the large holes of a box grater. Dump the shreds into the center of a clean kitchen towel, gather the corners, and twist tightly over the sink. Squeeze until almost no more liquid comes out. You should end up with about 1 packed cup of dry-ish shredded zucchini.
Whisk the dry ingredients: In your large mixing bowl, whisk together the flour, cocoa powder, baking soda, baking powder, and salt until everything is evenly combined and there are no cocoa lumps.
Mix the wet ingredients: In the medium bowl, whisk together the melted butter, oil, granulated sugar, and brown sugar until smooth and slightly glossy. Whisk in the eggs one at a time, then the vanilla and the buttermilk. The mixture should look smooth and a little pale when you are done.
Combine wet and dry: Pour the wet mixture into the dry mixture. Fold gently with a rubber spatula until just a few streaks of flour remain visible. Add the shredded zucchini and 1 ¼ cups of the chocolate chips. Fold just until combined. Do not keep mixing - overworking the batter will make the muffins tough.
Rest the batter: Cover the bowl with plastic wrap or a clean towel and let it sit at room temperature for 15 to 20 minutes. This resting period allows the starches to hydrate and the leavening to start working.
Fill the liners: Divide the batter evenly among the 12 muffin cups. Fill each liner all the way to the top - this is non-negotiable for the bakery dome effect. Sprinkle the remaining ¼ cup of chocolate chips over the tops, pressing them in very lightly so they stick.
Bake at high heat: Place the pan in the oven and bake at 425°F for exactly 5 minutes. Do not open the door. After 5 minutes, reduce the oven temperature to 350°F (without opening the door if you can manage it). Bake for another 14 to 17 minutes. The tops should spring back when you gently press them, and a toothpick inserted in the center should come out with a few moist crumbs - not wet batter.
Cool and release: Let the muffins cool in the pan for exactly 5 minutes. Transfer them to a wire rack to cool completely. If you leave them in the pan too long, the bottoms will steam and turn soggy.