Bring a large pan of salted water to the boil and add the cabbage leaves, carrots and shallots. Bring the water back to the boil and cook for two minutes then drain and quickly refresh the vegetables in a large bowl of iced water. Drain again, pat the vegetables dry then place them in a heatproof dish.
Place the vinegar, oil, garlic, sugar and coriander seeds into a small saucepan, bring to a boil then pour over the vegetables and leave to cool.
Preheat the oven to 180C/350F/Gas 4. Heat the butter and oil in a large frying pan. Season the quails with the salt and seal them in the frying pan until browned all over, basting with the butter as they brown. Transfer the quail to a roasting tin and roast in the oven for two minutes. Fry the chanterelles in the frying pan for one minute then season with salt and freshly ground black pepper.
To serve, place the quail on a plate with the chanterelles. Arrange the vegetables around the quail and drizzle over a little of the escabeche sauce. Garnish with the carrot tops.