Preheat the oven to 200°C.
Combine the chickpeas, sweetcorn, carrot, cornflour, ground cumin and seasoning in a large mixing bowl. Mash well until the mixture comes together as one, making sure you retains some texture. Make 4 large patties out of the mixture using lightly oiled hands.
Heat the remaining olive oil in a large ovenproof frying pan over a medium heat. Colour the patties in the oil on both sides until they are golden brown in colour, then transfer to oven and finish cooking there for 10 minutes.
Meanwhile, mix together all the ingredients for the tzatziki in a mixing bowl until well combined.
Heat the grill to hot and toast the bagel halves until golden brown on their cut sides. Remove and arrange on serving plates. Top with generous tablespoons of the tzatziki. Remove the vegetarian patties and sit on top of the tzatziki, garnishing them with the sprigs of dill. Place the other bagel halves on top and serve immediately.