Cut the haddock into four even-sized portions, leaving the skin on. Place the fillets in a saucepan, season and cover with milk. Bring to the boil and simmer for 2-3 minutes.
Meanwhile put the eggs in a thick-bottomed saucepan with the cream and 60g of the butter, season and cook on a very low heat for about 5 minutes, stirring constantly until the eggs are nice and creamy.
Melt the remaining butter in a pan with the herbs. Spoon the eggs onto warmed serving plates. Remove the haddock from the milk and remove the skin. Place the haddock on the eggs and spoon the butter and herbs on top.