Boiled eggs and potatoes in Bechamel sauce

4 medium potatoes
4 hard-boiled eggs
25 g butter
25 g flour
1/2 liter milk (double the quantity of milk if you need more bechamel)
ground nutmeg
salt

Boil the potatoes in their jacket for about 20 to 30 minutes until cooked.
Drain the potatoes and leave them to cool a little before peeling them and slicing them To prepare the Bechamel, melt butter in a large saucepan over medium-low heat.
Pour the flour over the melted butter and mix well to form a soft dough.
Maintaining a low heat, add progressively the milk to the dough, mixing well until all the milk is absorbed and continue pouring the milk until obtaining a sauce that is not not too thick (it should only be thick enough to coat the eggs and potatoes).
Season the bechamel with salt and nutmeg.
Slice the boiled eggs and add them to the bechamel.
Add the sliced potatoes to the bechamel sauce, mixing delicately so not to mash them.