Place grated zucchini in a sieve over the sink. Add salt and gently toss to combine; let sit for 10 minutes. Using a clean dish towel or cheese cloth, drain zucchini.
In a large bowl, combine zucchini, flour, parmesan, garlic and egg; season with salt and pepper, to taste.
Heat olive oil in a large skillet over medium high heat. Scoop tablespoons of batter for each fritter, flattening with a spatula, and cook until the underside is nicely golden brown, about 2 minutes. Flip and cook on the other side, about 1-2 minutes longer.
Serve sprinkled with oregano and salt