Hard boiled eggs gratin with Béchamel

Tasty gratin with hard boiled eggs and creamy béchamel sauce
Ingredients:
6 hard boiled eggs
50 g butter
50 g flour
500 ml milk
100 g grated cheese (Emmental or Groyere)
Salt and pepper to taste..
1 pinch of nutmeg
1 tablespoon chopped fresh parsley (optional)

Preparation:

Prepare the hard boiled eggs:
Cook the eggs in boiling water for about 9 minutes. Once cooked, immerse them in cold water, peel them and cut them in half. Arrange them on a gratin dish.
Prepare the béchamel sauce:
In a saucepan, melt the butter over medium heat. Add flour and whisk until you get a colorless red. Gradually pour in the milk, stirring constantly until you get a thick and creamy sauce. Season with salt, pepper and a pinch of nutmeg.
Assembling the Gratin:
Pour the béchamel sauce evenly over the hard-boiled eggs. Sprinkle with grated cheese on top.