Firstly, cook the haddock. Place the milk, bay leaves, thyme, peppercorns and cloves into a wide shallow pan and gently bring to the boil. Add the haddock, reduce the heat to a gentle simmer and poach for 5-6 minutes until the haddock is cooked. Remove from the heat, transfer the haddock to a plate and when cool enough to handle, remove the skin and flake into large pieces. Set the fish aside (discard the poaching liquor).
To make the hollandaise sauce, add the egg yolks to a large heatproof glass bowl set over a saucepan of simmering water. Whisk the yolks until pale and fluffy, taking care not to overcook them, and gradually whisk in half the melted butter, whisking constantly. Remove the bowl from the heat, add the white wine vinegar, then return the bowl to the heat and whisk in the remaining melted butter. Remove from the heat and allow to sit for a minute or two before gently folding in the whipped cream. Set aside.
Preheat the grill to high.
To make the omelette, beat the eggs in a large bowl and season with salt and pepper. Heat a 26cm non-stick frying pan over medium heat and add a knob of butter. Once melted, pour in the egg mixture and cook, stirring continually and slowly until the eggs are just beginning to set, but still a little runny in the middle.
Remove from the heat and scatter over the flaked haddock followed by the cheese. Pour over the hollandaise sauce.
Place the pan under the grill and cook for 2-3 minutes until the top is golden brown and bubbling.
Serve the omelette with green salad and chunks of crusty bread.