Preheat oven to 350°F (175°C). Grease a 9x5-inch loaf pan with butter or nonstick spray, then line with a parchment sling for easy removal.
Wash and dry the zucchini. Grate on the small or medium holes of a box grater. Gently squeeze the shredded zucchini with your hands or a clean towel to remove excess moisture without wringing it completely dry. If using very large zucchini, scoop out any large seeds before grating. Set aside.
In a large mixing bowl, whisk together the flour, granulated sugar, brown sugar, baking soda, baking powder, salt, cinnamon, and nutmeg (if using). Break up any clumps of brown sugar so the mixture is evenly combined.
In a separate medium bowl, whisk the eggs until well combined. Add the oil, Greek yogurt or sour cream, and vanilla, and whisk until smooth and slightly glossy.
Pour the wet mixture into the bowl with the dry ingredients. Gently stir with a spatula or wooden spoon until just combined; a few small streaks of flour are fine. Do not overmix.
Add the shredded zucchini, chopped nuts, and chocolate chips (if using). Gently fold until the zucchini is evenly distributed and no dry pockets remain. The batter will be thick but slightly loose from the zucchini moisture.
Scrape the batter into the prepared loaf pan and smooth the top. If desired, sprinkle about 1 tablespoon of granulated sugar over the top for a crackly crust.
Bake on the middle rack for 55–65 minutes, or until the top is deeply golden brown and a toothpick inserted into the center comes out mostly clean with a few moist crumbs. If the top browns too quickly, tent loosely with foil for the last 10–15 minutes.
Let the zucchini bread cool in the pan for 10–15 minutes. Use the parchment sling to lift it onto a wire rack and cool completely for the cleanest slices.
Slice with a serrated knife into thick or thin pieces. Serve plain, with butter, or with cream cheese. Enjoy for breakfast, snacks, or dessert.