1 cup dried porcini or mixed wild mushrooms (not shiitake)
4 cups water
3 leeks, white and light green parts, rinsed, trimmed
1 medium onion
3 ribs celery
1 large carrot, peeled
1/2 cup (1 stick) unsalted butter
1 lb white mushrooms, thinly sliced
1 Tbsp caraway seeds
4 cups beef broth, vegetable broth or water
5 large potatoes, peeled, cut into 1/2-inch chunk
4 cups whole milk
Salt and freshly ground black pepper, to taste
1 cup sour cream
1/4 cup unbleached, all-purpose flour
2 tsp sweet Hungarian paprika
Place dried mushrooms and 4 cups water in a saucepan. Bring to a boil, then simmer, uncovered, for 30 minutes. Strain the mushrooms, reserving the cooking liquid. Coarsely chop the mushrooms and set aside.
In a food processor, finely mince the leeks, onion, celery and carrot. Melt the butter in a stockpot over medium-high heat, and add the minced vegetables. Sauté 5 minutes. Reduce the heat to medium, add the fresh and dried mushrooms and caraway seeds. Continue cooking until the vegetables are very tender, 15-20 minutes.
Meanwhile, pour the reserved mushroom liquid into a pot, being careful to leave any sediment behind. Add the broth and potatoes. Simmer until the potatoes are tender, 20-25 minutes. Add the potatoes and liquid to the sautéed vegetables, and mash half of the potatoes against the side of the pot with a large spoon to help thicken the soup.
Add the milk to the soup and heat through, and season to taste with salt and pepper. Whisk the sour cream, flour and paprika together in a small bowl until smooth. Stir into the soup pot to blend. Cook the soup a few minutes over low heat, being sure not to let the soup boil, or it will curdle. Serve hot.