Preheat oven to 375°F (190°C). Grease or line a 12-cup muffin tin.
Place shredded zucchini in a clean kitchen towel and gently squeeze out excess moisture.
In a medium bowl, whisk together flour, baking powder, baking soda, salt, garlic powder, oregano, and black pepper.
In a large bowl, whisk together eggs, milk, and olive oil.
Stir the shredded zucchini into the wet ingredients.
Add the dry ingredients to the wet ingredients and mix until just combined.
Fold in 1 cup of Parmesan cheese.
Divide the batter evenly among the muffin cups, filling each about ¾ full.
Sprinkle the tops with the remaining Parmesan cheese.
Bake for 20–25 minutes, or until golden brown and a toothpick inserted in the center comes out clean.
Cool in the pan for 5 minutes before transferring to a wire rack.