Shred the zucchini using the large holes of a box grater. Place it in a colander, toss with 1/2 teaspoon of the salt, and let it sit for 10 minutes.

Transfer the zucchini to a clean kitchen towel or paper towels and squeeze very well until most of the liquid is removed.

In a medium bowl, whisk the eggs. Add the flour, Parmesan, onion, garlic, parsley, black pepper, and remaining 1/2 teaspoon salt. Stir until combined.

Add the squeezed zucchini and mix until evenly coated. The mixture should be thick enough to scoop.

Heat 1 to 2 tablespoons olive oil in a large skillet over medium heat.

Drop heaping spoonfuls of the mixture into the skillet and gently flatten them into small rounds.

Cook for 3 to 4 minutes on the first side until golden brown and set around the edges. Flip carefully and cook for another 3 to 4 minutes.

Transfer to a paper towel-lined plate or wire rack. Add more oil as needed and repeat with the remaining batter.

Serve warm with sour cream or Greek yogurt, chopped chives, and lemon wedges if desired.