- 1
Melt the butter in a small saucepan, stir in the flour, then gradually add the milk. Keep stirring until the sauce is smooth and lump-free. Season with salt, pepper, and grated nutmeg.
- 2
Spread half the sauce over two of the bread slices. Lay two slices of ham on each, top with half the cheese, then close the sandwiches with the remaining bread slices.
- 3
Heat a frying pan over medium heat and add the butter. Once it's foaming nicely, lay in the sandwiches cheese-side down. Fry until they start to turn golden, pressing them gently together with a spatula.
- 4
Flip the sandwiches carefully and fry the other side until golden.
- 5
Transfer the sandwiches to an ovenproof dish. Spoon the rest of the béchamel over the top and scatter over the remaining cheese. Bake in the middle of the oven at 200 °C for about 10 minutes, until the cheese is golden and bubbling.
- 6
Wipe out the pan and heat it again with a little butter. Fry the eggs until the whites are set but the yolks are still runny.
- 7
Take the sandwiches out of the oven and plate them up. Top each one with a fried egg, a sprinkle of parsley, and serve straight away while everything's hot.