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1
Heat the oil and unsalted butter in a saucepan over medium-low heat until it reaches 220 degrees F. Reduce the heat to low, add the shallots, and cook until they are a rich golden brown, 30 to 40 minutes.
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2
The temperature should stay below 260 degrees F. Stir the shallots occasionally to make sure they brown evenly.
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3
Remove them from the oil with a slotted spoon, drain well, and spread out to cool on paper towels.
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4
Once they have dried and crisped, they can be stored at room temperature, covered, for several days.
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5
Peel the turnips to remove the waxy skins and cut them into generous 1-inch chunks.
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6
Place them in a saucepan with water to cover and 1 teaspoon of salt.
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7
Bring to a boil and simmer, covered, until easily pierced by a paring knife, about 35 minutes.
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8
Drain.
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9
In a separate saucepan, heat the milk and salted butter over low heat until the butter has melted and the milk just begins to simmer.
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10
Puree the turnips in several batches in a food processor fitted with the steel blade.
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11
With the motor running, add the melted butter and milk in a steady stream.
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12
The turnips should be smooth.
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13
Return the puree to the saucepan, season with 1 teaspoon salt and the pepper, and reheat, stirring, over medium heat.
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14
Serve piping hot, sprinkled generously with crispy shallots.
