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Grate the parsnips into a bowl and add the flour and dill. Beat 2 of the eggs and add them to the bowl. Season and set aside.
Heat oven to its lowest setting. Pour the milk into a saucepan and add the haddock, skin-side up. Cover, bring slowly to the boil, then turn off the heat and poach for 5 mins. Discard the milk and haddock skin. Put the fish in a bowl and mix in the horseradish and lemon zest – as you stir, the fish will flake. Put the spinach in a casserole dish, then push to one side, pour over 3 tbsp boiling water and season. Put the haddock in the other side, cover with foil and put in the oven to keep warm.
Heat the oil in a large frying pan, add three large mounds of the parsnip mixture, flatten with the back of a fish slice and fry for 3-4 mins on each side until golden. Transfer to a baking tray lined with kitchen paper and keep warm in the oven. Repeat with the remaining mixture.
Bring a large pan of water to a simmer, crack in the eggs and poach for 2-3 mins, then drain on kitchen paper. Divide the latkes between plates, spoon over the fish and spinach and top with an egg. Season and serve with dill fronds and lemon wedges.