The amount of oil here may seem like a lot, but it’s necessary to crisp and brown the mushrooms. Don’t worry — most of the oil will come out of the mushrooms once they’re done, and you can easily leave it on the baking sheet. I love king oysters and chanterelles for their beauty and taste, but they’re not cheap — use the best mushrooms you can afford and know that good ol’ buttons will be tasty too.
Place the dried mushrooms in a large bowl and cover with 1 1/2 cups boiling water. Let the mushrooms steep until rehydrated, at least 30 minutes.
Meanwhile, heat the oven to 425 degrees. Place the fresh mushrooms, arranged by type, on a large rimmed baking sheet. Drizzle with the olive oil, add the thyme and season with salt and pepper. Toss the mushrooms to evenly coat with the seasonings, then spread out in an even layer. Roast the mushrooms, undisturbed, until a deep golden brown where they touch the pan and tender and crisp at their edges, 35 to 40 minutes.
Use a slotted spoon to lift out the porcinis and transfer them to a cutting board. Finely chop the mushrooms, then transfer to a small bowl. Add half the shallots, then stir in the vinegar and sugar until dissolved; refrigerate until ready to use. Slowly pour 1 cup of the soaking liquid into a small bowl; discard the rest along with any sediment in the bottom of the bowl.
Meanwhile, melt the butter in a small saucepan over medium heat. Add the remaining shallots and the garlic and cook, stirring, until soft, about four minutes. Sprinkle in the flour and stir constantly for 30 seconds to cook off the raw taste. While whisking, pour in the reserved mushroom soaking liquid and heavy cream and bring to a boil. Continue cooking until thickened, about one minute. Remove the pan from the heat, let cool for 10 minutes, then whisk in the sour cream and season with salt and pepper.
Once the mushrooms come out of the oven, spoon the cream sauce on the bottom of a serving platter and rearrange the mushrooms by type on top. Dollop small spoonfuls of the pickled mushrooms over the roasted mushrooms and sprinkle with fresh thyme leaves before serving.
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