Preheat oven to 400°F. Line a 12-cup muffin tin with parchment liners.
Grate the zucchini on the fine side of a box grater. You should have about 1 cup of shredded zucchini. Do not peel.
Cup the grated zucchini in your hands over the sink and give it one gentle squeeze to release surface water. It should still be damp, not dry.
In a large bowl, whisk together flour, cocoa powder, baking soda, baking powder, and salt.
In a separate bowl, whisk together egg, brown sugar, oil, Greek yogurt, and vanilla until smooth and glossy.
Pour the wet mixture into the dry. Stir with a rubber spatula until just combined (about 5 folds). Do not overmix.
Fold in the squeezed zucchini and 1 cup chocolate chips until evenly distributed. Reserve a few chips for topping.
Divide batter evenly among the 12 muffin cups, filling each to the very top. Press a few reserved chocolate chips onto the tops.
Bake at 400°F for 5 minutes. Without opening the oven, reduce temperature to 350°F and bake for another 15-18 minutes, until a toothpick inserted in the center comes out with a few moist crumbs.
Let muffins rest in the tin for exactly 5 minutes, then transfer to a wire rack. Immediately sprinkle with flaky sea salt. Cool completely before storing.