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1
Put the horseradish in a saucepan with water to cover and bring to a boil; simmer for about 5 minutes, then drain and rinse with cold water.
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2
Meanwhile, peel the potatoes and rinse them; slice them thinly with a knife or mandoline.
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3
Preheat the oven to 400F.
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4
Layer the potatoes and horseradish in a large nonstick, ovenproof skillet or roasting pan, sprinkling the layers with salt and pepper.
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5
Dot with the butter, then add enough half-and-half to come about three-quarters of the way up to the top.
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6
Turn the heat under the gratin to high and bring to a boil.
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7
Turn the heat to medium-high and cook for about 10 minutes, or until the level of both liquid and vegetables has dropped somewhat.
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8
Put in the oven and cook, undisturbed, until the top is nicely browned, about 10 minutes.
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9
Turn the oven down to 300F and continue cooking until the potatoes and horseradish are tender (a thin-bladed knife will pierce them with little or no resistance), about 10 minutes more.
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10
Serve immediately or keep warm in the oven or over very low heat for up to 30 minutes.
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11
Substitute 1/4 pound of good-quality Gruyere, grated, for the horseradish and add an additional pound of potatoes.
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12
Layer the two as described in step 2, but instead of bringing the whole mixture to a boil on top of the stove, put the pan directly into the preheated oven and bake for 1 to 1 1/2 hours, until tender.
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13
Run the gratin under the broiler for 30 seconds or so to crisp, then serve hot or warm.