In a food processor, whizz the chickpeas with the egg for a few mins until almost a purée, but some bits remain. Spoon into a bowl and stir in the mince, spices, two-thirds of the garlic, the chilli and coriander. Season well and form into 12 small fritters.
Heat the oil in a non-stick frying pan and cook the fritters in batches for 4 mins on each side, until crisp on the outside and cooked through.
Top each wrap with a good handful of shredded lettuce, tomato, red onion and 3 fritters. Mix the yogurt with the remaining garlic and spoon a little over the fritters. Wrap up and tuck in, with chips on the side, if you like.