Heat 2 tbsp olive oil in a heavy bottomed saucepan over a medium heat. Add the onion and cook for 5 minutes until slightly softened. Add the celery, carrot, parsnip and parsley with seasoning and cook, stirring regularly, for a further 15 minutes until very soft. Add the tomato purée, paprika and a splash of water with the passata, allspice berries and bay leaves and cook for a further 20 minutes. It should be thick but the vegetables should all be very soft.
Season the carp fillets and dust with flour. Heat the remaining olive oil in a large frying pan over a medium heat. Put the fillets in the pan skin side down and cook for 4-5 minutes, or until the skin is golden. Flip the fish over and continue to cook for 2 minutes until cooked through. Squeeze over half the lemon juice.
Just before serving, stir most of the dill leaves through the sauce, reserving some to garnish. Stir through the remaining lemon juice and season to taste.
Serve the fish with the vegetables. This can be eaten straight away but is traditionally also left in the fridge overnight and eaten at room temperature the next day.