Preheat the oven to 350°F. Place the rack in the centre of the oven. Line a 9×5×3-inch loaf pan with parchment paper overhanging the sides. Lightly butter the paper.
Sift together the flour, cocoa, baking soda and baking powder into a large bowl with the salt, cinnamon and cardamom. Stir in the zucchini and chocolate chunks. Whisk together the eggs, sugar, brown sugar, olive oil, buttermilk and vanilla in another bowl. Pour this into the zucchini mixture and stir just until combined.
Scrape the batter into the prepared pan and bake for 50–60 minutes, until the bread has risen and a toothpick inserted in the centre comes out clean but with a few crumbs clinging to it. Let the loaf cool in the pan on a wire rack for 20 minutes, then remove the loaf from the pan and let cool completely on the rack.
Store the zucchini bread in an airtight container at room temperature for up to 3 days, or freeze for up to 2 months.
Note: If the shredded zucchini is full of moisture, squeeze it dry in a clean dishcloth before adding to the batter.