Preheat the oven to 350 degrees F.
In a large skillet, heat 1 tablespoon of the oil over medium heat. Add the leeks and 2 tablespoons water; season with salt and pepper. Cook, stirring occasionally, until tender but not browned, about 8 minutes. Add the thyme and then the cream and cook until the liquid thickens, about 2 minutes; set aside.
In a 2-quart shallow baking dish, arrange the sweet potato in overlapping layers. Spread the leek mixture evenly over the potatoes. Arrange the apples in an overlapping layer on the leeks. Brush the apples with the remaining tablespoon of oil and sprinkle with the Parmesan. Cover tightly with aluminum foil and bake 40 minutes. Uncover and continue to bake until the Parmesan is golden brown and melted, about 20 minutes more. The tip of a paring knife should easily pierce the apples and potatoes. Let cool 10 minutes before serving.
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