Cook the potatoes in boiling salted water until soft.
Drain well and mash. Add the cream and butter, then season with salt and pepper and nutmeg. Mix well until smooth and creamy. Taste, adding more seasoning if required, then set to one side.
For the parsley sauce, heat the butter in a heavy-based pan over a very low heat then stir in the parsley. Cook for about ten minutes.
Add the flour and stir well. Cook, stirring regularly, for about three minutes. Do not let the mixture brown.
In another pan, bring the milk to the boil. Pour this into the "roux" (the butter and flour mixture) a little at a time, whisking or beating after each addition until completely smooth. Whisk in single cream, to taste. Bring the sauce to the boil, then reduce the heat and simmer over a low heat for 5-6 minutes.
While the sauce is cooking, pre-heat the oven to 200C/400F/Gas 6 and generously butter a deep ovenproof dish.
Cut the haddock and salmon into serving piece, lay in the dish, season lightly and squeeze over a little lemon juice.
Pour the hot parsley sauce over the top, place the quartered eggs evenly over the sauce and spoon over the mashed potatoes.
Bake for 35-40 minutes, until the top is crisp and brown. Serve at once.