Position a rack in the center of an oven and preheat to 350 degrees. Butter a shallow 2 quart ceramic baking dish.
In a large bowl, combine the cream, eggs, salt, pepper and nutmeg and whisk just until blended. Add the potatoes and toss gently until evenly mixed.
Transfer to the prepared baking dish. Using your fingertips, spread the potatoes in an even layer, pressing them lightly so they absorb the liquid. Sprinkle the cheese and then the parsley evenly over the top.
Cover the dish tightly with foil and bake for 45 minutes. Remove the foil and ocntinue baking until the top is golden, the gratin is bubbling and the potatoes are for tender, 15 to 20 minutes or more.