Place mushrooms in a medium bowl. Pour the boiling water over mushrooms. Cover and let stand for 15 minutes. Meanwhile, in a 4-quart Dutch oven cook pancetta in hot butter over medium heat until lightly browned. Using a slotted spoon, remove pancetta; drain on paper towels, reserving drippings in Dutch oven. Chop pancetta; set aside.
Add sweet onions, garlic, brown sugar, and salt to the Dutch oven. Cook and stir over medium-low heat until golden, stirring occasionally.
Meanwhile, using a slotted spoon, remove porcini mushrooms from the liquid (do not discard liquid). Chop mushrooms; set aside. Reserve all but about 1/4 cup of the mushroom liquid (discard the liquid at the bottom of the bowl, which may be gritty).
When the onions are golden, stir in mushrooms and Marsala wine. Cook until most of the liquid has evaporated. Add the reserved mushroom liquid, the beef broth, thyme, rosemary, and bay leaf. Bring to boiling; reduce heat. Simmer, uncovered, about 30 minutes. Discard thyme and rosemary sprigs and the bay leaf.