Cook potatoes in boiling salted water until soft.
Drain potatoes and mash with 150ml cream, 55g butter, seasonings, and nutmeg until smooth.
Heat 85g butter in a pan over low heat and stir in parsley for ten minutes.
Stir in 30g flour and cook for three minutes without browning.
Whisk 570ml boiling milk into the roux, add a splash of cream, and simmer for 5-6 minutes.
Preheat oven to 200°C and butter a deep ovenproof dish.
Cut fish into pieces, place in the dish, season, and add lemon juice.
Pour sauce over fish, add quartered eggs, and top with mashed potatoes.
Bake for 35-40 minutes until crisp and golden.