Preheat the oven to 200C/Gas 6.
Peel the potatoes and parsnips and thinly slice using a mandolin or in a food processor using the thin blade attachment.
Pour the cream and milk into a saucepan and add the onion, garlic, salt and nutmeg.
Bring to a simmer and then add the parsnips. Cook for two minutes then add the potatoes and cook for a further 5 minutes.
Put a layer of the potatoes and parsnips into an ovenproof dish and sprinkle with a little cheese, then add the rest of the vegetables on top and pour over any remaining cream sauce. Grate a little more nutmeg if you wish over the top and then sprinkle the remaining cheese.
Cover with foil which you have greased with oil or butter on the side that will touch the gratin and bake for one hour.
Remove the foil and brown the gratin for a further 20 minutes.