Combine the bay leaves, thyme, vinegar, sugar, onions and carrot in a pot, bring to the boil and season. Simmer for 15 minutes.
Spread out the herring fillets on a large chopping board and sprinkle with cinnamon, salt and pepper. Coat the fish with the mustard and then add the dill. Close the fillets on themselves and coat with the flour.
Heat the oil and butter in a nonstick frying pan and fry the fish for 1 minute on each side. Place in a casserole and pour the hot brine over the top. Let the fish soak for at least 6 hours, but preferably overnight.
To serve, the herring can either be eaten hot or cold. To heat, place the casserole in a very hot oven for 5 minutes.