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1
In a large saucepan, heat the oil until shimmering.
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2
Add the shallots and cook over moderate heat, stirring occasionally, until softened, about 8 minutes.
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3
Add the wine and cook until reduced to 1/4 cup, about 25 minutes.
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4
Add the cream and bring to a boil.
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5
Simmer over moderately low heat until thickened and reduced to 4 1/2 cups, about 1 1/2 hours.
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6
Strain the cream sauce through a fine sieve into a medium bowl, then season with salt and pepper.
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7
Bring a large saucepan of salted water to a boil.
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8
Add the carrots and cook over high heat until crisp-tender, about 5 minutes.
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9
Drain and pat dry.
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10
Melt 2 tablespoons of the butter in the same saucepan.
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11
Add the ginger and cook over moderate heat until fragrant, about 2 minutes.
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12
Add the carrots and cook, tossing, until coated.
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13
Add 1 1/2 cups of the cream sauce and simmer over moderately low heat until the carrots are tender and the sauce is slightly reduced, about 4 minutes.
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14
Transfer to a bowl, cover and keep warm.
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15
Clean the saucepan.
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16
Fill the same saucepan with water and bring to a boil.
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17
Add the onions and cook over high heat until crisp-tender, about 5 minutes.
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18
Drain and rinse in cold water.
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19
Trim the root ends and pull off the skins.
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20
Return the peeled onions to the saucepan.
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21
Add 1 1/2 cups of the cream sauce and the horseradish.
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22
Simmer over moderate heat until the sauce is slightly reduced and the onions are tender, about 2 minutes longer.
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23
Transfer to a bowl, cover and keep warm.
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24
Melt the remaining 4 tablespoons of butter in a very large, deep skillet.
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25
Add the garlic and cook over moderately high heat until lightly browned.
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26
Add the mushrooms and thyme and cook, stirring occasionally, until the liquid is evaporated and the mushrooms are golden, about 15 minutes.
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27
Stir in the remaining 1 1/2 cups of cream sauce, season with salt and pepper and cook until the sauce is slightly reduced and the mushrooms are very tender.
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28
Transfer to a bowl.
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29
This can be made ahead, refrigerated, and reheated.