Put the haddock, bay leaf and onion in a pan; cover with the milk. Simmer gently for 20 minutes; leave to cool. Drain the fish, reserve the infused milk, and discard the bay and onion. Flake the fish and set aside; discard the skin and bones.
For the mornay sauce, melt the butter, add the flour and cook for 10 minutes, stirring. Gradually add the infused milk and stir until smooth. Simmer gently for 5 minutes, stirring continuously, until thickened. Season, stir in the cheese and egg yolks and take off the heat to cool.
Preheat the grill to high. Divide the fish and butter between 2 x 12cm ovenproof frying pans and cook until the butter has melted. Add 2 lightly beaten eggs to each pan and cook for 1–2 minutes until they begin to firm up, then stir in the crème fraîche and chives. Spoon the sauce on top, then grill for about 5 minutes until golden and bubbling. Slide the omelettes onto plates to serve.