To make the béchamel sauce melt 3 tbsp butter in a saucepan.
Stir in the flour and cook for 1 minute.
Gradually whisk in the milk until smooth and thickened.
Season with salt, pepper, and nutmeg. Set aside.
Start to assemble the sandwiches. Spread béchamel on 6 slices of bread.
Add ham and half the cheese.
Top with the remaining bread slices.
Spread a little béchamel on top and sprinkle with the rest of the cheese.
Pre-heat the grill.
Melt 2 tbsp butter in a frying pan.
Place the sandwiches in batches in the frying pan and fry until golden on both sides.
Transfer to a baking tray and grill for 3–5 minutes until the cheese topping bubbles.
Fry 6 eggs sunny-side up in a separate pan.
Place one fried egg on each sandwich.
Serve hot with a fresh salad or crispy potatoes