Preheat oven to 325°. In a small saucepan, bring cream, salt, and nutmeg to a simmer. Remove from heat and set aside.
Lay half the potatoes evenly in a shallow 2 1/2-qt. baking dish, followed by half the parsnips and all the shallot and celery root. Top with half the cheese. Add remaining parsnips, then remaining potatoes. Pour warm cream over vegetables. Sprinkle evenly with remaining cheese.
Bake until bubbling, golden brown, and tender when pierced, about 1 1/4 hours. Let sit 10 minutes before serving.
Make ahead: Up to 2 days; reheat at 325° until center is warm, about 30 minutes.
Note: Nutritional analysis is per serving.