In a food processor, pulse the chickpeas, parsley, garlic, cumin, and ¼ teaspoon each salt and pepper until coarsely chopped and the mixture comes together when gently squeezed.
Form the mixture into eight ½-inch-thick patties and coat with the flour, tapping off any excess.
Heat the oil in a nonstick skillet over medium-high heat. Cook the patties, turning carefully, until golden brown, 2 to 3 minutes per side.
In a small bowl, whisk the yogurt, lemon juice, and ¼ teaspoon each salt and pepper.
Divide the greens, tomatoes, onion, and chickpea patties among plates. Drizzle with the dressing and serve with the pita chips (if using).