How to Make It
Preheat the oven to 375°. Lightly butter a 9-by-13-inch baking dish. In a medium bowl, whisk the cream with the garlic, shallot, nutmeg, salt and pepper. Stir in 1 cup of the grated cheese.
In a large bowl, gently toss the beets with one-fourth of the cream mixture. Arrange the beets in the baking dish in an even layer, overlapping them slightly. Scrape any remaining cream from the bowl over the beets. Repeat this process with the sweet potatoes, Yukon Golds and turnips, using one-fourth of the cream mixture for each vegetable. Press a sheet of parchment paper on top of the turnips, then cover the dish tightly with foil.
Bake the gratin for about 1 hour and 30 minutes, until the vegetables are tender. Uncover and top with the remaining 3/4 cup of cheese. Bake for about 15 minutes longer, until golden on top. Transfer the gratin to a rack and let cool for at least 15 minutes before serving.