Soak the herring fillets in water for 24 hours, changing the water 3 times. Then dry them well with a towel.
Put the fillets in a deep dish. Add the bay leaves, sliced onion, cloves, peppercorns, thyme, and sliced carrots. Cover them well with olive oil Cover, refrigerate, and marinate for 5 days.
Just before serving, boil the potatoes for about 10 minutes, or until cooked through. Peel and slice them 1/8 to 1/4-inch thick and arrange the slices from 2 potatoes on each of 6 plates. Top each serving with 2 herring fillets, drizzle with some of the marinade oil and scatter on some of the carrots and onion slices. Garnish each plate with two slices of lemon, the chopped tomato, onion, parsley and parsley sprig.