Preheat the oven to 400°F. Peel the root vegetables. Using a mandolin, thinly slice the vegetables into slices about 1/6 inch thick. If some of the vegetables are much larger than the others, they can be cut half before layering.
In a mixing bowl, combine the cream, flour, chopped fresh thyme, kosher salt, nutmeg, and pepper. Whisk until smooth.
Lightly grease an 9x13" or oval baking dish. Arrange the root vegetables in small groups of 4 or 5 slices in the baking dish. Start by fanning out a small group of rutabaga slices. Follow with a small group of celery root and then finish with the parsnip. Repeat the pattern down each row in the baking dish to ensure a balanced presentation and flavour.
Pour the cream mixture evenly over the vegetables. Cover with foil and bake for 50 to 60 minutes until the vegetables are almost tender. Remove the foil and top with the shredded cheese.
Bake for another 10 to 15 minutes until the vegetables are completely tender and the gratin is browned. Garnish with more chopped fresh thyme and enjoy!