Grate the zucchini and place it in a colander. Sprinkle with 1/2 teaspoon salt and let it sit for 10 minutes.
Wrap the zucchini in a clean kitchen towel and squeeze out as much liquid as possible.
In a mixing bowl, combine the zucchini, egg, breadcrumbs, Parmesan, black pepper, and a pinch of extra salt if desired. Mix thoroughly.
Form the mixture into 12 small patties.
For stovetop cooking: Heat the olive oil in a frying pan over medium-high heat. Cook the fritters for 3 to 4 minutes on each side until they turn golden brown.
For oven baking: Preheat the oven to 425°F. Place the fritters on a parchment-lined baking sheet, brush them with oil, and bake for 15 to 20 minutes, turning halfway through.
For air frying: Preheat the air fryer to 400°F. Arrange the fritters in a single layer, spray lightly with oil, and cook for 8 to 10 minutes, flipping once.