Shred the zucchini using a box grater or food processor, then place it in a clean kitchen towel or cheesecloth and squeeze firmly to remove as much liquid as possible—this step is crucial to prevent a soggy loaf. While the zucchini drains, measure out all your dry ingredients (flour, cinnamon, baking soda, baking powder, salt, and nutmeg) into one bowl, and measure the wet ingredients (brown sugar, olive oil, Greek yogurt, eggs, and vanilla) into another bowl. Coarsely chop the walnuts into roughly 1/4-inch pieces and set aside.
While you're preparing the zucchini, preheat your oven to 350°F and lightly coat a loaf pan (or 9x5-inch baking dish) with cooking spray, ensuring all corners are covered to prevent sticking. In your bowl with the wet ingredients, whisk together the brown sugar, olive oil, Greek yogurt, eggs, and vanilla until well combined and smooth—the mixture should be creamy and uniform. I like to use room-temperature eggs here because they incorporate more smoothly and create a better texture in the final loaf.
Add the dry ingredient mixture from Step 1 to the wet ingredient mixture from Step 2, and stir gently with a spatula or wooden spoon until just combined—do not overmix, as this can develop gluten and make the bread tough. The batter should look slightly lumpy; this is intentional and will result in a more tender crumb. Fold in the squeezed zucchini and chopped walnuts until evenly distributed throughout the batter.
Pour the batter into your prepared pan, smoothing the top gently with a spatula so it bakes evenly. Place the pan in your preheated 350°F oven and bake for 70–75 minutes, until a toothpick inserted into the center comes out with just a few moist crumbs (not wet batter). The top should be golden brown and a crack may form down the center, which is completely normal. I always start checking around the 65-minute mark to avoid over-baking, especially if your oven runs hot.
Remove the bread from the oven and let it cool in the pan on a wire rack for about 10–15 minutes, then carefully turn it out onto the rack to cool completely before slicing. This resting period allows the crumb to set and makes the bread easier to slice cleanly.