There's a knack to getting this old classic right, as the acid in the potatoes tends to make the cream curdle. To avoid this, you need to blanche the potatoes in milk, and make sure that the oven doesn't get too hot. You can also add a tiny bit of flour to the mix, and if you use waxy potatoes, the starch content will help to stop further curdling.
Incidentally, the Dauphiné area in the French Alps is known for its rich dairy pastures- and that's why the dish is called Dauphinoise. Nothing to do with the French Monarchy or the Revolution.
Pre-heat the oven to 160C. Line a baking tin with greaseproof paper, and butter the paper. Slice a raw garlic clove in two, and rub it over the paper.
Peel and slice your potatoes. For this dish, I infinitely prefer the waxy varieties, and if possible, I would avoid floury varieties at all cost. Slice them very thinly. I use a Magimix for this.
Boil some milk in a saucepan, whisking to stop it burning. "Blanche" the sliced potatoes in the milk for five minutes; this will help to remove the acid from the potatoes. In another pan, pour 150ml of full-fat milk and a 142ml carton of double cream and add a sprig of thyme. Blend two teaspoons of flour with a splash of milk, and mix thoroughly, so that there are no lumps. Mix this into the creamy milk. Bring to a near boil, and put to one side.
Layer the baking tin with the potato slices- so that they look a bit like fish scales. Season with sea-salt, black pepper and nutmeg. Arrange another layer on top, but with the shapes facing in the other direction. Season. Five or six layers should be about right. Pour over the milky cream mixture (first removing the thyme sprig) and then grate fresh parmesan all over the top.
Bake for about an hour, or until the potatoes are properly cooked, and the top is golden. Take out of the oven, leave to stand for a few minutes, and then cut into squares.