Grate the zucchinis and sprinkle them with salt. Let them sit for about 10 minutes, then squeeze out as much liquid as possible with a clean towel.
In a bowl, whisk the egg, flour, parmesan, parsley, garlic, and pepper. Add the zucchini and stir until combined.
Heat olive oil in a large skillet over medium heat. Scoop small portions of the mixture into the pan and flatten them gently with a spatula.
Cook for 3 to 4 minutes per side until golden brown and crispy. Place on paper towels to drain before serving.