Preheat the oven to 400°F.

Wash, peel and cut the potatoes in thin slices. Use a mandoline or food processor, if you have them, to make sure the slices are all about the same thickness.

In a medium size saucepan, melt the butter with half cup of milk. Once melted, mix in the flour and whisk until smooth. Cook for a couple of minutes.

Stir in the rest of the milk (preferably warm) some at the time while whisking. Make it smooth. Cook the white sauce until bubbly and thickened, about 5 minutes, stirring occasionally. Season with salt (about 1 teaspoon) and nutmeg (half teaspoon).

Grease a round 10.5-inch quiche pan (or 2 quarts baking dish). Spread a layer of the potatoes slices on the bottom of the baking dish. Season with salt and pepper, and top with some of the besciamella sauce.

Make two more layers of potato and white sauce. Sprinkle with Parmesan cheese on top.

Uncover and bake for an additional 30 minutes or until the potatoes are tender.

If you need, broil on high for one minutes until nicely browned.

Let stand 5 to 10 minutes before serving, so the sauce will set a little when cooling down.

Sprinkle the top with chopped parsley and serve.