Preheat your oven to 350°F (175°C). Grease and flour a 9×5-inch loaf pan or line it with parchment paper.
In a medium bowl, whisk together the all-purpose flour, baking soda, baking powder, salt, ground cinnamon, ground nutmeg, and ground cloves until well combined.
In a large bowl, whisk the granulated sugar, light brown sugar, and vegetable oil until fully combined.
Add the eggs one at a time to the sugar and oil mixture, whisking well after each addition.
Stir in the vanilla extract.
Fold the grated zucchini into the wet ingredients.
Add the plain Greek yogurt and mix until just incorporated.
Gradually add the dry ingredients to the wet ingredients, folding gently until just combined. Do not overmix.
Pour the batter into the prepared loaf pan and smooth the top with a spatula.
Bake for 50 to 60 minutes, or until a toothpick inserted into the center comes out clean or with just a few moist crumbs.
Remove the bread from the oven and let it cool in the pan for 10 minutes.
Transfer the zucchini bread to a wire rack to cool completely before slicing.