Preheat the oven to 350°F (177°C). Grease a 9 × 5-inch loaf pan and line it with parchment paper, leaving some paper over the sides to make the loaf easier to remove.
Wash the zucchini and trim off the ends. Do not peel it. Grate it using the large holes of a box grater.
Measure 1½ cups of packed shredded zucchini. Do not wring it completely dry. If the zucchini is unusually watery, place it in a clean towel and give it one gentle press. The goal is to remove excess liquid without drying out the zucchini.
In a medium bowl, whisk together the flour, baking powder, baking soda, salt, cinnamon, and nutmeg. Set the bowl aside.
In a large bowl, whisk together the granulated sugar, brown sugar, oil, applesauce, Greek yogurt, eggs, and vanilla extract. Whisk until the mixture looks smooth and evenly combined.
Add the shredded zucchini to the wet ingredients and stir gently with a spatula. The mixture may look quite moist. This is normal and helps create a tender loaf.
Add the dry ingredients to the wet mixture in two additions. Fold gently with a spatula until no large streaks of flour remain. Do not overmix the batter. A few small lumps are fine. Overmixing can make the loaf dense or tough. If using nuts, chocolate chips or dried fruit, fold them in at the end. For blueberries, toss them with one teaspoon of flour before adding them to the batter.
Pour the batter into the prepared loaf pan and smooth the top. Bake for 55 to 70 minutes, or until: the top is golden brown, a toothpick inserted into the center comes out with a few moist crumbs, the center feels set rather than liquid, and an instant-read thermometer registers approximately 200–205°F (93–96°C). Begin checking the loaf at around 55 minutes. Baking time can vary depending on the pan, oven and moisture content of the zucchini. If the top becomes dark before the center is baked, loosely cover the loaf with aluminum foil during the final 15 minutes.
Let the bread cool in the pan for 45 to 60 minutes. Then carefully transfer it to a wire rack and allow it to cool completely before slicing. The crumb continues to set as the loaf cools. Cutting it too early can make the center appear wet or cause the slices to break apart.