Preheat oven to 400 degrees. Butter 3 quart baking dish.
In large saucepan over medium heat, melt butter. Add garlic and cook for 1 minute Add cream, salt, pepper and nutmeg and heat just until bubbles form around edges of pan, 5 minute Remove from heat and let stand 10 minute.
Arrange (slightly overlapping) a layer of parsnips in dish. Top with layer of sweet potatoes, then celery root. Pour half of sauce over vegetables and sprinkle half the cheese and herbs.
Cover with foil, bake for 1 hour on baking sheet.
Remove foil and press gratin down with spatula.
Bake until veggies are tender and top is golden brown, 15 to 30 minutes.