Preheat the oven to 200°C.
Place the haddock in an ovenproof dish with 100ml milk, butter, bay leaves, and peppercorns.
Poach the fish in the oven for 10-12 minutes and set aside to cool.
Mix the crème fraîche, lemon zest, parmesan, and most of the chives with seasoning.
Heat the butter and 15ml of oil in a frying pan and add the beaten eggs.
Flake the haddock into pieces while removing the skin and any bones.
Spread the cream mixture over the eggs, add the fish, and bake for 4-5 minutes.
Dress the watercress with remaining oil and lemon juice to serve with the omelette.