This is hands down the best potato gratin I've ever eaten. The interesting technique of turning the potatoes in the pan while they are cooking is what makes the difference. I adapted this recipe after enjoying a similar one at a long-gone bouchon in Lyon, France - my favorite city. French gratins are a bit different from most of the ones I grew up eating. For one thing, they have less cheese - sometimes none. —ChefJune
Heat the oven to 400 degrees F. Rub the inside of an oval porcelain gratin dish (about 14 x 9 x 2 inches) with the garlic. Arrange the potatoes in an even layer in the dish.
Mix the milk, eggs and salt and pour over the potatoes. Sprinkle generously with pepper.
Bake, occasionally cutting the crust that forms on top and gently folding it into the potatoes, until the gratin is golden, about 55 minutes. [This step is VERY important.]
Remove the gratin dish from the oven, sprinkle with the grated cheese, then dab the gratin with crème fraîche. Return the dish to the oven and bake until the top is very crisp and golden, about 15 minutes.