Lightly salt grated zucchini & let sit in a colander for 10 minutes.
Squeeze to remove excess moisture. In a large bowl, combine all the ingredients, except oil, and mix well.
Heat oil in a skillet over medium-high heat. Drop heaping tablespoons of mixture into oil; cook a few minutes on each side, until golden. Place on paper towels & sprinkle with parmesan cheese while hot.