Drain, rinse, and pat chickpeas very dry with kitchen towels.
Mash chickpeas roughly with a fork or potato masher — about 80% broken down, some texture remaining. Do not blend smooth.
Add grated onion, garlic, cumin, oregano, parsley, flour, egg (if using), salt, and pepper. Mix to combine. Mixture should hold a ball when pressed.
Form into 16-18 patties, about 1.5 inches wide and 1/2 inch thick. Press firmly.
Heat olive oil in a wide skillet over medium heat. Fry in batches, 3-4 minutes per side, until deeply golden and crisp. Do not crowd the pan.
Drain briefly on paper towels. Serve immediately with tzatziki and lemon wedges.