Step 1 Melt the butter in a heavy pot over medium heat. Add the shallots and garlic and sweat them until tender, about 2 minutes. Add the cream, milk, salt, pepper and nutmeg. Bring the mixture to a simmer, then remove from heat to steep while you prepare the vegetables.
Step 2 Heat the oven to 450 degrees. Peel and very thinly slice the celery roots and parsnips (about one-eighth inch thick), either using a mandoline or by hand. In a 9-inch gratin dish or deep dish pie plate, spread one-third cup creme fraiche. Add a layer of parsnips, then a layer of celery root, then spoon over about 3 tablespoons of the cream mixture. Repeat the process until the last layer reaches the top of the dish.
Step 3Cut a piece of parchment the same size as the top of the gratin dish or pie plate, lay it over the top layer, then cover the dish with aluminum foil, sealing around the edges. Bake for 45 minutes. Remove from the oven and let sit for 30 minutes. Reduce the oven temperature to 375 degrees. Top the gratin with the remaining 2 tablespoons creme fraiche spread evenly over the top. Sprinkle on the cheeses and bread crumbs. Bake for 20 to 30 minutes until the cheese is melted and the gratin is nicely browned. Serve hot.