Soak the dried mushrooms in 1 cup warm water for 30 minutes, then lift them out and strain the liquid. Finely chop the mushrooms. Add the soaking liquid to the mushroom stock in a large saucepan. Bring to a simmer.
Heat the butter in a wide soup pot, add the diced shallots, and cook over medium heat until soft and translucent, 3 to 5 minutes. Add the rice and cook, stirring frequently, for 1 minute. Add the mushrooms and wine and simmer until the wine is absorbed, stirring a few times, then add 2 cups stock, cover and cook at a lively simmer until it's absorbed. Begin adding the stock in 1/2 cup increments, stirring constantly until each addition is absorbed before adding the next. When the rice is cooked, stir in the parsley, cheese, and an additional 1 or 2 tablespoons of butter. Taste for salt and season with pepper.
Soak porcini in a bowl of warm water for 30 minutes. Set aside.
Heat oil in a soup pot. Add the onion, carrots, and celery. Saute over medium-high heat, stirring occasionally, until the onion is well browned, about 15 minutes. Scrape the bottom of the pan to loosen juices that have collected there. Add porcini, soaking liquid, remaining ingredients and 9 cups of water. Bring to a boil, then lower heat and simmer, partially covered, for 45 minutes. Strain.