Preheat the oven to 350°F (177°C). Line two baking sheets with parchment paper and set aside.
Grate the zucchini and place it in a clean kitchen towel or several layers of paper towels. Sprinkle a tiny pinch of salt over the shreds, wrap up the towel and press or squeeze firmly to remove excess moisture. Transfer the drained zucchini to a small bowl and set aside.
In a medium bowl whisk together the flour, cocoa powder, baking soda, fine salt, and instant espresso powder until evenly combined.
In a large bowl whisk the melted butter and brown sugar vigorously until smooth and slightly glossy. Whisk in the egg yolk until blended, then stir in the vanilla extract. Fold the squeezed zucchini into the wet mixture.
Add the dry mixture to the wet ingredients and stir with a spatula just until no streaks of flour remain — don’t overmix. Fold in the chocolate chips until distributed.
For slightly thicker, less-spreading cookies, chill the dough in the refrigerator for 15 minutes (optional). Then use a 1 1/2-tablespoon scoop (or a rounded tablespoon) to drop mounds about 2 inches apart onto the prepared sheets.
Bake one sheet at a time in the preheated oven for 10 to 12 minutes, until the centers are set but still soft. Rotate the pan halfway through baking if your oven runs hot.
Let the cookies rest on the baking sheet for 5 minutes, then transfer to a wire rack to cool completely. While warm, sprinkle with flaky sea salt if desired and drizzle with a little melted chocolate for extra gloss.