Preheat oven to 325F, and prepare a 9x5 loaf pan with parchment paper, then set aside.
Place shredded zucchini on a paper towel while you prepare the other ingredients, so it can absorb some of the moisture while you prepare the batter.
In a large mixing bowl, whisk together flour, cocoa powder, baking powder, salt, espresso powder, if using.
In a medium bowl, whisk together brown sugar, Greek yogurt, oil, eggs and vanilla, then transfer to the dry ingredients and mix until no dry streaks.
Lightly blot top of the shredded zucchini, and stir it in along with any amount of the chopped chocolate; I like to reserve a small amount for the top.
Pour the finished batter into your prepared baking pan and top with remaining chocolate.
Bake for about 60 minutes, or until a toothpick comes out clean. Set on a wire rack and let cool completely before removing from the pan to slice and enjoy.
Notes
Don't Overmix: Mix the wet ingredients into the dry ingredients just until combined, then gently fold in the zucchini.
Check the Center: A toothpick or cake tester inserted into the center should come out clean or with a few moist crumbs. Just be careful not to mistake melted chocolate for uncooked batter. If you like to use a thermometer, the middle should be around 202F, but not higher than 205F.
Let It Cool: Give the loaf time to cool completely before slicing. Cutting into it while it's still hot can make the center appear underbaked.
Blot Lightly: Lightly blot the shredded zucchini to remove excess moisture, but don't wring it dry. Some of that moisture is exactly what helps give the loaf its great texture.
Room Temperature: Once completely cool, wrap the loaf tightly or store it in an airtight container at room temperature for up to 2 days out of direct sunlight.
Refrigerator: Store the loaf, covered, in the fridge for up to 5 days.
Freezer: Wrap the whole loaf or individual slices tightly, then place in a freezer-safe container for up to 3 months. Individual slices are especially handy for thawing as needed.