Heat the oven to 350 degrees F. Line a baking sheet with a silicone baking mat or parchment paper to protect the baking sheet from spills and make for easy cleanup.
Peel the potatoes and slice them on a mandoline into 1/8-inch-thick slices. Or, using a chef's knife, carefully slice the potatoes thinly and evenly.
Arrange the potatoes in a medium casserole dish in overlapping layers, seasoning with salt and pepper as you go. Place the dish on the prepared baking sheet. Combine the milk, heavy cream, thyme, garlic and nutmeg in a medium heavy-bottomed saucepan. Bring to a gentle simmer over medium heat. Pour over the potatoes. Sprinkle the cheese over the top.
Bake until the potatoes are tender and the top is bubbling around the edges and a deep golden brown, about 1 hour. (If it starts to brown too deeply, cover the top of the dish with aluminum foil.) Let cool 10 minutes before serving.
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