There are a number of versions of this regional dish from Dauphine, some without the topping of grilled cheese. The word gratin originally referred not to the topping, but to the crispy bits at the bottom.
Wash, peel and rinse the potatoes. Cut in half then thinly slice (just under 5mm thick) with a sharp knife. Butter a shallow ovenproof dish and layer the potatoes, garlic, grated cheese, nutmeg and seasoning between the layers, leaving a little cheese for the top. Mix the cream and milk together then pour over the top of the potatoes. Sprinkle with the remaining cheese. Bake for 50-60 minutes or until the potatoes are completely cooked and the liquid absorbed. If the top browns too much, cover loosely with foil. Leave to rest for 10 minutes before serving.
If you want to make this in advance of a dinner party, then bake about 40 minutes, cool and cover with foil. Finish off the cooking just before serving main course.