Put the grated carrot and courgette in a clean tea towel and squeeze out the excess liquid. Transfer to a bowl and add the mushrooms, oregano, parsley, cayenne pepper, ketchup, soy sauce and 100g/3½oz of the breadcrumbs. Mix well and season with a little salt and pepper.
Put the chia seeds (if using) in a small bowl with 3 tablespoons of cold water and leave for 5 minutes until thickened. Add the mixture to the vegetables in the bowl or, if using egg substitute, mix the powder with 2 tablespoons of cold water then add it to the mixture. Shape the mixture into 8 burgers and coat each burger in the remaining breadcrumbs.
Heat the oil in a large frying pan over a medium heat and fry the burgers in batches for 2–3 minutes on each side until golden and crisp. Serve with soup or salad.
The cooked burgers can be frozen (once cooled) for up to 2 months. Defrost, then reheat in a preheated oven at 180°C/350°F/Gas 4 for about 20 minutes, or until heated through.