Preheat oven to Gas 5, 190°C, fan 170°C. Heat the oil in a pan. Add the shallots, celery and carrot and cook for 10 minutes until softened. Stir in the cumin, chickpeas and parsley, and cook for a further minute. Put into a food processor and whizz for 3-4 seconds. Pour into a bowl and stir in the egg. Season well.
Scatter the sesame seeds into a shallow dish. Use a spoon to take walnut-sized amounts of the chickpea mixture and shape into little patties to make 16 in total. Press each side into the sesame seeds. Bake on a baking sheet lined with nonstick baking paper for 20 minutes until golden and firm.
Arrange on a plate, spoon the tzatziki into separate bowls and serve with the lemon wedges and parsley sprigs.
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