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1
Cover potatoes generously with well-salted cold water in a large pot and bring to a boil.
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2
Reduce heat and simmer potatoes, partially covered, until they are just barely tender, 20 to 25 minutes.
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3
Transfer potatoes to a colander using a slotted spoon, rinse under cold water to stop the cooking, and dry.
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4
Chill potatoes on a plate, uncovered, at least 8 hours.
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5
Peel potatoes and coarsely grate into a large bowl.
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6
Add thyme, 1 1/2 teaspoons salt, and 3/4 teaspoon pepper, then drizzle with 2 tablespoons butter and toss mixture well.
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7
Heat oven to 375F with rack in middle.
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8
Heat oil and 1 tablespoon butter in skillet over medium-high heat until foam subsides, then add potato mixture and tamp it down firmly in skillet with a rubber spatula, smoothing the top.
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9
Reduce heat to medium and cook potato cake, covered with a lid, until edges begin to turn golden, about 5 minutes.
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10
Remove lid, then bake potato cake, uncovered, 10 minutes.
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11
Brush top of potato cake with remaining 2 tablespoons butter.
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12
Turn on broiler and broil potato cake, 4 to 5 inches from heat, until golden brown, 3 to 7 minutes.
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13
Remove skillet from oven carefully (wear oven mitts!).
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14
Run the rubber spatula around the edge of the cake to loosen it from the skillet.
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15
Invert a large round heat-proof plate over skillet and invert potato cake onto plate.
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16
Cut into wedges and serve.
