2 tablespoons unsalted butter
2 1/2 pounds turnips, trimmed and left unpeeled
1 tablespoon chopped thyme
1/2 tablespoon chopped savory
1 1/2 teaspoons kosher salt
Rounded 1/8 teaspoon cayenne
1 cup heavy cream
1 cup grated Parmigiano-Reggiano
Preheat oven to 450°F with rack in middle.
Melt butter in an ovenproof 12-inch heavy skillet, then cool.
Slice turnips paper-thin with slicer, then arrange one third of slices, overlapping tightly, in skillet, keeping remaining slices covered with dampened paper towels. Sprinkle with about a third of thyme, savory, kosher salt, and cayenne. Make 2 more layers.
Cook, covered, over medium heat until underside is browned, about 10 minutes. Add cream and cook, covered, until center is tender, 20 to 25 minutes.
Sprinkle evenly with cheese, then bake, uncovered, until golden and bubbling, 10 to 15 minutes. Let stand 5 minutes before serving.