Shred the zucchini using the largest holes of a box grater or a shredding disk of a food processor.

Spread the shredded zucchini on a clean kitchen towel, sprinkle with salt and let sit for 10 minutes to draw some of the moisture out.

Gather the sides of the towel together, twist, and squeeze until all the liquid has been pressed from the zucchini. Transfer to a mixing bowl.

Add the Parmesan cheese, eggs, 1/3 cup of the flour, salt and a few grinds of black pepper and combine thoroughly.

Heat 3 tablespoons of oil in a large pan over medium-high heat and make a test fritter by adding about 2 tablespoons of batter to the hot oil. If the fritter spreads to more than three inches in diameter, add another tablespoon of flour to the batter and try again.

Once the batter consistency is right, fry the fritters in batches, using about 2 tablespoons of the zucchini mixture for each one. Be sure to leave plenty of room between them for easy turning.

Fry until golden brown and the edges of the fritters hold together fairly well when you try to flip them over, 2 to 3 minutes per side. You may need to add more oil to the pan after a couple of batches.

Place finished fritters on several thicknesses of paper towels and gently blot the excess oil.

Transfer to a baking sheet in a single layer and keep warm in 250°F oven until ready to serve.