Place the porcini in a medium bowl and pour the boiling water over. Let soak until softened, 20 to 30 minutes. Drain, reserving the soaking water. Coarsely chop the mushrooms and set aside.
In a large heavy pot, heat the oil over medium-high heat. Add the onion and cook until softened, 5 to 7 minutes. Add the mushrooms and stir briefly, then add the bay leaves, pepper, the reserved mushroom soaking water, the water or stock, and rice. Raise the heat and bring to a boil. Partially cover, lower the heat to medium-low, and simmer for 10 minutes.
Add the carrots and potatoes and bring back to a boil, then simmer, partially covered, over medium-low heat for 30 minutes, or until tender. If the liquid looks low, add
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