Heat oven to 350°F. Line a 9×5-inch loaf pan with a parchment sling and lightly grease the exposed sides.
Grate the zucchini on the large holes of a box grater. Measure 1 3/4 cups, then wrap in a clean kitchen towel and wring out well until no liquid drips. Fluff with a fork and set aside.
In a large bowl, whisk together the flour, cocoa, baking powder, baking soda, fine sea salt, and espresso powder until evenly combined.
In a separate bowl, vigorously whisk the eggs and granulated sugar for 30–45 seconds until slightly pale. Whisk in the oil, sour cream, and vanilla until smooth and glossy.
Fold the squeezed zucchini into the wet mixture. Add the dry mixture and stir gently with a spatula just until a few floury streaks remain.
Fold in 2/3 cup chocolate chips. Scrape the batter into the prepared pan, smooth the top, and tap the pan once on the counter to release air. Sprinkle the remaining 2 tablespoons chips over the surface and add a light pinch of flaky sea salt.
Let the filled pan rest on the counter for 5 minutes to hydrate the cocoa, then bake for 55–60 minutes, rotating the pan after 40 minutes. If the top darkens too quickly, tent loosely with foil. A tester inserted near the center should come out with a few moist crumbs, not wet batter.
Cool in the pan for 15 minutes, then lift out using the parchment and cool completely on a rack, at least 1 hour, before slicing with a serrated knife.