Dreamy Creamed Carrots, Onions and Mushrooms

In a large saucepan, heat the oil until shimmering. Add the shallots and cook over moderate heat, stirring occasionally, until softened, about 8 minutes. Add the wine and cook until reduced to 1/4 cup, about 25 minutes. Add the cream and bring to a boil. Simmer over moderately low heat until thickened and reduced to 4 1/2 cups, about 1 1/2 hours. Strain the cream sauce through a fine sieve into a medium bowl, then season with salt and pepper.

Bring a large saucepan of salted water to a boil. Add the carrots and cook over high heat until crisp-tender, about 5 minutes. Drain and pat dry. Melt 2 tablespoons of the butter in the same saucepan. Add the ginger and cook over moderate heat until fragrant, about 2 minutes. Add the carrots and cook, tossing, until coated. 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. Transfer to a bowl, cover and keep warm. Clean the saucepan.

Fill the same saucepan with water and bring to a boil. Add the onions and cook over high heat until crisp-tender, about 5 minutes. Drain and rinse in cold water. Trim the root ends and pull off the skins. Return the peeled onions to the saucepan. Add 1 1/2 cups of the cream sauce and the horseradish. Simmer over moderate heat until the sauce is slightly reduced and the onions are tender, about 2 minutes longer. Transfer to a bowl, cover and keep warm.

Melt the remaining 4 tablespoons of butter in a very large, deep skillet. Add the garlic and cook over moderately high heat until lightly browned. Add the mushrooms and thyme and cook, stirring occasionally, until the liquid is evaporated and the mushrooms are golden, about 15 minutes. 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. Transfer to a bowl. Serve all of the vegetables.