1. In a saucepan, bring quinoa and broth to a boil over medium-high heat. Cover, reduce heat to low and cook until all broth has been absorbed, about 15 minutes. Let cool slightly.
2. In a food processor, process bread until fine bread crumbs form. Add chickpeas, quinoa, egg, cilantro, cumin, chile, salt and pepper and process in short bursts until mixture is finely chopped. Shape mixture into 4 patties. Brush patties with oil and cook in a nonstick frying pan over medium-high heat until golden, about 4 minutes per side.
3. Serve patties with pitas and, if desired, greens, avocado, tomato and mayonnaise or yogurt.