Put the water, onion, carrot, bay leaf, parsley stalks, peppercorns and lemon rind in a saucepan. Cover and bring to the boil, then reduce the heat and simmer on low heat for 30 minutes.
Preheat the oven to 110°C. Strain the water into a large frying pan, discarding the vegetables, and bring to the boil. Add the fish pieces, skin side up, and poach on low heat for 3 minutes, or until a toothpick will slide in easily; take care not to overcook. Lift the fish out of the pan with a fish slice and place, skin side down, in a shallow roasting tin. Cover with foil and put in the oven to keep hot.
Poach the eggs in the stock remaining in the frying pan for about 3 minutes or until whites are set. Lift them out with a fish slice and place one on top of each piece of fish and cover again with foil. Boil the stock remaining in the pan until reduced to about 1 cup.
Meanwhile, in a separate saucepan, bring the cream to the boiling point and then stir in 2 tablespoons of the chopped parsley. Strain the reduced stock through a fine sieve into the cream and continue to boil it on low heat for 2–3 minutes.
Carefully lift the fish pieces and eggs onto heated individual plates. Strain the juices from the roasting tin into the parsley sauce, taste and adjust seasoning, if necessary. Spoon the sauce over the eggs and sprinkle with the remaining parsley. Serve the fish with fresh or toasted wholemeal bread.