1. Slice the shallots crosswise into very thin rings. In a saucepan, heat the oil with the butter over medium-low heat until it begins to bubble. Reduce the heat to low, add the shallots and cook until they are a rich golden brown, about 30-40 minutes. Stir the shallots occasionally while they are cooking to make sure they brown evenly.

2. Remove the shallots from the oil with a slotted spoon and drain on paper towels. Once the shallots have dried and crisped, in about 15 minutes, they can be stored in a cool place, covered, for several days. Serve the shallots at room temperature .

3. Peel the turnips to remove their waxy skins, and cut them into generous 1-inch chunks. Place them in a saucepan with water to cover and 1 teaspoon of salt. Bring to a boil and simmer, covered, until easily pierced by a paring knife, about 35 minutes.

4. In a separate saucepan, heat the milk and butter over low heat until the butter has melted and the milk just begins to simmer.

5. Drain the turnips, and puree (in several batches, if necessary) in a food processor. With the motor running, add the melted butter and milk in a steady stream. The turnips should be very smooth.

6. Return the turnip puree to the saucepan, season with 1 teaspoon salt and the pepper and reheat, stirring over a medium flame. Serve piping hot, sprinkled generously with crispy shallots.

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