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1
Preheat oven to 400F.
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2
Tightly wrap beets in double layers of foil to make 3 packages (2 large beets or 4 medium per package) and roast on a baking sheet in middle of oven until tender, 1 1/4 to 1 1/2 hours.
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3
Cool to warm in foil packages (the steam makes beets easier to peel), about 30 minutes.
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4
While beets are roasting, cook onions in butter in a 12-inch heavy skillet, covered, over moderately low heat, stirring occasionally, until soft, about 20 minutes.
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5
Add salt, sugar, and vinegar and cook, uncovered, stirring occasionally, until onions are very tender and caramelized to deep brown, about 20 minutes more.
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6
Add wine and boil, stirring occasionally, until liquid is reduced to about 2 tablespoons, 3 to 5 minutes.
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7
Transfer mixture to a food processor and pulse to a coarse puree.
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8
Return to skillet and season with salt and pepper, then reheat onion marmalade, covered, over low heat.
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9
While marmalade is reheating, peel beets, discarding stems and root ends, and cut crosswise into 1/8-inch-thick slices with slicer.
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10
Divide warm marmalade among 6 dinner plates and spread evenly in a very thin layer to cover bottom of each plate using offset spatula.
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11
Arrange beet slices in 1 layer over onion, overlapping them only enough to cover onions.
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12
Drizzle 2 teaspoons oil over each serving and season with pepper.
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13
Shave 4 to 6 curls of Parmigiano-Reggiano with a vegetable peeler over beets on each plate.
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14
Serve immediately.
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15
Available at many cookware stores and Uwajimaya (800-899-1928).
