Peel the potatoes, wipe clean with a damp cloth and cut them into thin slices.
Do not wash or soak them in water as this would remove the starch essential to the correct consistency of the dish.
Pour the milk into a large saucepan, season with salt, freshly ground pepper and nutmeg to taste and add the butter cut into small pieces.
Place over a medium heat, beat with a birch (wire) whisk and bring slowly to boiling point, add the potatoes and the cream gradually, reduce the heat and simmer very slowly for 10 minutes, stirring frequently.
Rub a large gratin dish with the cut clove of garlic, butter it generously and pour in the potato mixture.
Scatter the cheese on top and bake very slowly for 1 1/2 hours until a crisp brown crust has formed.