Place a third of the grated carrot into a food processor with the onion, garlic, chickpeas, ground and fresh coriander, egg and seasoning. Whiz to a paste and set aside.
Heat 1 tablespoon of oil and fry the remaining carrot for about 10 minutes, stirring from time to time. Add this cooked carrot to the whizzed paste. Stir in the flour and mix well. Check seasoning and adjust accordingly. With wet hands, divide the mixture into 8 and shape into burgers. Cover and chill for 30 minutes.
Preheat the grill or BBQ. Brush the burgers with the remaining oil and cook for about 5 minutes on each side or until golden and crisp.
Toast the burger buns or warm on the BBQ. Mix the yoghurt, chives and remainder of the carrot together. Spread yoghurt mixture onto each bun, top with a few leaves of spinach and insert the cooked burger.