01 - Preheat oven to 375°F (190°C). Butter a 9x13-inch baking dish.
02 - Peel and thinly slice parsnips, carrots, rutabaga, Yukon Gold potato, celeriac, and leek. Combine in a large bowl.
03 - Melt butter in a medium saucepan over medium heat. Whisk in flour continuously for 1 minute to form a roux.
04 - Gradually whisk in whole milk and heavy cream, cooking until smooth and thickened, about 4 to 5 minutes.
05 - Stir in Dijon mustard, freshly grated nutmeg, salt, and black pepper. Remove from heat.
06 - Arrange half the sliced vegetables in the baking dish. Pour half the sauce over vegetables and sprinkle half the Gruyere.
07 - Layer remaining vegetables, cover with the remaining sauce, then top with the rest of the Gruyere and all of the Parmesan cheese.
08 - Cover dish with foil and bake for 35 minutes.
09 - Remove foil and bake for an additional 15 minutes until the top is golden and vegetables are tender.
10 - Allow gratin to rest 10 minutes before garnishing with chopped parsley and serving.