1. Peel the potatoes and cut them into pieces. Cook them in salted water. Drain them, let them evaporate, and mash them with a splash of milk and a knob of butter. Season with pepper, salt, and nutmeg.
2. Clean the mushrooms with a brush and cut them into small pieces. Peel the parsnip and also cut it into small pieces. Cook the parsnip and mushrooms together in hot butter. Season with pepper and salt.
3. Cut the haddock into 3 equal parts lengthwise. Place 2 parts across the other part. Season the fish with pepper and salt.
4. Preheat the oven to 180°C (350°F).
5. Arrange the steamed vegetables in the center of the fish. Fold the bottom part of the fish inward, then the other 2 pieces, to form a ballotine. Place them, closure side down, in an ovenproof dish. Melt some butter and drizzle it over the fish.
6. Bake for 15 minutes in the preheated oven.
7. Peel and finely chop the shallots. Chop the chives and capers. Mix the minced shallot with the capers and chives.
8. Place a fish ballotine on each plate and garnish it with the shallot mixture. Form quenelles with the mashed potatoes and place them next to the fish. Drizzle with melted butter.