Dust the flathead pieces lightly in flour. Heat a little olive oil in a large frying pan and fry the fish on both sides until a light golden brown. Remove from the pan and drain on kitchen paper.
Heat a little more oil and some butter in the same pan and add the carrots. Sauté over a low heat. Add a splash of stock or water and sauté slowly until the carrots are tender.
In a separate pan, bring the wine to the boil. Remove from the heat and leave to cool. When cold, stir in the vinegar.
Arrange some pieces of fish in a smallish, non-reactive dish and top with the carrots. Sprinkle on the peppercorns, tuck the bay leaves in among the fish pieces and season with salt and pepper as you go. Continue layering the fish and carrots until they are all used up. They should fit rather snugly.
Pour the wine–vinegar mixture over the top. Cover and refrigerate for at least one day before serving.