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Pour the tomatoes into a heatproof dish that fits in your air-fryer. Stir the balsamic vinegar, apple cider vinegar and honey together, then stir this mixture into the tomatoes. Season the tomatoes with salt and pepper and stir again, before adding the chickpeas, chorizo and sweet peppers and giving one more stir.
Preheat the air-fryer to 180ºC. Place the dish in the preheated air-fryer and cook for 12 minutes, stirring once during cooking.
Serve hot with freshly chopped parsley scattered over.