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Heat oven to 400 degrees. Seasoning each layer with salt and pepper as you go, layer the potatoes in a 10- or 12-inch ovenproof skillet.
Dot the top with 2 tablespoons butter. Pour in half-and-half. (It should come about 3/4 of the way to the top.)
Bring to a boil over medium-high heat. Reduce to low and cook for 10 minutes, uncovered, until the half-and-half has reduced by about half.
Transfer to the oven and bake until the top is golden brown, about 10 minutes. Reduce heat to 300 degrees and cook until the potatoes are fork tender and the top is nicely browned, about 8 minutes more. Top with grated cheese and return to the oven until the cheese is melty and golden brown, about 3 to 5 minutes. Sprinkle with a pinch of nutmeg, if using, and serve.