Preheat the oven to 180°C/gas mark 4. Heat the 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 stalks with seasoning and cook, stirring regularly, for a further 15 minutes until very soft. Add the tomato puree, 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.
Lay the carp on a roasting tray and brush with the olive oil. Season on the outside and the inside and roast for 15 minutes, until just cooked.
Just before serving, stir most of the dill leaves through the sauce, reserving some to garnish. Stir through the lemon juice and season to taste.
Garnish the fish with the lemon slices and serve 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.