01 - Preheat oven to 375°F. Butter a 9x13-inch baking dish thoroughly.
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, continuing to stir until mixture thickens, about 4 to 5 minutes. Remove from heat.
05 - Incorporate Dijon mustard, nutmeg, salt, and black pepper into the sauce, blending well.
06 - Arrange half of the sliced vegetables evenly in the buttered dish. Pour half of the sauce over the vegetables and sprinkle with half of the grated Gruyere cheese.
07 - Layer remaining vegetables on top. Pour remaining sauce over them. Finish by adding the rest of the Gruyere followed by all the Parmesan cheese.
08 - Cover the dish with foil and bake for 35 minutes.
09 - Remove foil and bake an additional 15 minutes until the top is golden and vegetables are tender.
10 - Allow gratin to rest for 10 minutes before garnishing with chopped parsley and serving.