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1
Place the dried porcini mushrooms in a heat-proof bowl and cover with 6 cups of boiling water to rehydrate, let sit 1/2 hour.
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2
For the stock, clean and chop the leeks, peel and dice the carrot, and clean and chop the celery. Reserve.
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3
Clean the fresh mushrooms by brushing them with a clean cloth, pull off the stems and add them to the chopped vegetables for the stock. Slice the mushroom caps and reserve for sauteing later.
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4
When the porcini are done soaking, skim them from the bowl with your hands and wring them dry. Give them a rough chop and reserve for sauteing. Line a strainer with cheesecloth and place it over a bowl. Carefully pour the porcini soaking liquid through the strainer, collecting the clean broth in the bowl beneath, you should have a round 4 cups.
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5
In a medium, heavy duty casserole, over medium heat, place one tablespoon of olive oil, with 2 tablespoons of butter. Add the veggies, mushroom stems, 3 sprigs of thyme, 1 sprig of tarragon, a few grinds of white pepper, and a large pinch of salt. Saute until the ingredients are nicely caramelized. Deglaze with the white wine and let it fully reduce, add the mushroom stock and 2 cups of chicken stock, bring to a gently boil, then lower the heat and let simmer for 1/2 hour.
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6
While the stock is cooking, saute the sliced mushroom caps in three batches, one for each type of mushroom, in 1 tablespoon olive oil, and 2 tablespoons butter. When nicely browned, combine in a bowl. Take 1 cup of the mixed, sauteed mushrooms and set aside, place the rest in the bowl of a blender.
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7
When the stock is done, pour through a strainer to remove the solids, you should be left with about 4 cups of finished stock. Take 2 cups of the stock and add it to the blender with the mushrooms. Blend on low speed for about 30 seconds to very finely chop the mushrooms. Pour the mixture into a clean sauce pan.
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8
To this pan, add an additional 1 1/2 cups of finished stock, and 1 1/2 cups of heavy cream, 1 teaspoon of freshly minced thyme, and heat over low-medium flame to a simmer. Check for seasoning, adding salt and pepper to taste.
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9
Thicken the soup as desired by adding the arrowroot slurry in 2-3 additions, stopping when you achieve the consistency you want.
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10
Finish the soup by adding the reserved 1 cup of sauteed mushrooms, and 1-2 tablespoons of Madeira to taste. Recheck the seasoning, ladle into warmed bowls, and top with a liberal sprinkling of freshly chopped tarragon.
