Preheat the oven to 400 degrees F. Butter a 13 by 9-inch casserole dish with 1 teaspoon of the butter.
Starting with the rutabagas, layer 1/3 of the vegetables, apples and onions in the prepared dish, very lightly seasoning with salt and pepper and dotting with butter between each. Top with a layer of Fontina. Repeat the layering, seasoning, and cheese, ending with cheese on top.
In a saucepan, bring the cream, chicken stock, and thyme to a boil. Remove from the heat and pour over the vegetables. Bake in the oven, covered, for 30 minutes. Uncover and continue baking until nearly all the cream is absorbed, about 30 to 40 minutes. Sprinkle with the Parmesan and bake until golden, all the liquid is absorbed, and the vegetables are fork tender, about 15 minutes.
Remove from the oven and let cool at least 15 minutes before serving.
Yield: 8 to 10 servings