Prepare. Heat the oven to 150°C (130°C fan, gas mark 2) with a shelf on the highest rung. Butter the gratin dish well.
Slice. Peel the potatoes and slice them very thinly, about 3mm, using a mandoline or sharp knife.
Rinse and dry. Swish the slices in a bowl of cold water to remove some starch, then dry them very thoroughly in a clean tea towel.
Layer. Arrange a layer of potatoes in the dish. Sprinkle over some of the crushed garlic, salt and pepper. Add a second layer of potatoes and more seasoning.
Add the cream and milk. Mix the cream and milk together and pour evenly over the potatoes.
Finish. Sprinkle with freshly grated nutmeg and dot the butter in flecks over the surface.
Bake. Bake on the highest shelf for 1½ hours, until golden on top and the potatoes are completely tender.
Rest. Let the dish stand for 10 minutes before serving.