Place a large pan of water on a high heat. Add the vinegar. Bring to a rapid boil, then reduce the heat to a simmer, whisk the water and crack in two of the eggs. Cook for 3 minutes, until the eggs are just poached and holding their shape. Remove with a slotted spoon and put straight into a bowl of iced water. Repeat with the remaining two eggs. These eggs will keep happily in the fridge for up to two days.
Meanwhile, pour the milk into a large frying pan and add the sliced onion and bay leaf. Bring to a simmer over a medium heat, then carefully place the haddock into the milk, skin side down. Simmer for 2 minutes, then turn over and simmer for another 2 minutes, until the smoked haddock is just cooked through and tender. Lift the haddock out of the milk. Carefully remove and discard the skin and keep the haddock warm. Strain the poaching milk through a sieve into a small clean pan to remove the onion and bay leaf. Put over a medium heat and whisk in the mustard and lemon juice and the cornflour mixture. Bring to the boil to thicken, whisking continuously. Season to taste, remove from the heat and keep warm, whisking in the chopped chives at the last minute.
Place the grated potatoes, melted butter, parsley and seasoning in a bowl and mix well. Heat a large non-stick frying pan over a medium to low heat and spray the base with olive oil. Place large spoonfuls of the mixture into the pan, flatten with a fish slice and cook for 5–6 minutes on each side, until crisp and golden brown. You will need 12 in total, allowing three per serving. Spray the pan with olive oil for each batch.
Place the cooked poached eggs into a fresh pan of boiling water for 1 minute to reheat them.